Mathematik, Informatik und Statistik - Open Access LMU - Teil 01/03

A nonlinear structural errors-in-variables model is investigated, where the response variable has a density belonging to an exponential family and the error-prone covariate follows a Gaussian distribution. Assuming the error variance to be known, we consider two consistent estimators in addition to the naive estimator. We compare their relative efficiencies by means of their asymptotic covariance matrices for small error variances. The structural quasi score (SQS) estimator is based on a quasi score function, which is constructed from a conditional mean-variance model. Consistency and asymptotic normality of this estimator is proved. The corrected score (CS) estimator is based on an error-corrected likelihood score function. For small error variances the SQS and CS estimators are approximately equally efficient. The polynomial model and the Poisson regression model are explored in greater detail.

We investigate a stationary random cofficient autoregressive process. Using renewal type arguments tailor-made for such processes we show that the stationary distribution has a power-law tail. When the model is normal, we show that the model is in distribution equivalent to an autoregressive process with ARCH errors. Hence we obtain the tail behaviour of any such model of arbitrary order.

With the introduction of compulsory long term care (LTC) insurance in Germany in 1995, a large claims portfolio with a significant proportion of censored observations became available. In first part of this paper we present an analysis of part of this portfolio using the Cox proportional hazard model (Cox, 1972) to estimate transition intensities. It is shown that this approach allows the inclusion of censored observations as well as the inclusion of time dependent risk factors such as time spent in LTC. This is in contrast to the more commonly used Poisson regression with graduation approach (see for example Renshaw and Haberman 1995) where censored observations and time dependent risk factors are ignored. In the second part we show how these estimated transition intensities can be used in a multiple state Markov process (see Haberman and Pitacco, 1999) to calculate premiums for LTC insurance plans.

In this paper we analyse data originating from the German Deep Drill Program. We model the amount of 'cataclastic rocks' in a series of measurements taken from deep drill samples ranging from 1000 up to 5000 meters depth. The measurements thereby describe the amount of strongly deformed rock particles and serve as indicator for the occurrence of cataclastic shear zones, which are easily speaking areas of severely 'ground' stones due to movements of different layers in the earth crust. The data represent a 'depth series' as analogue to a 'time series', with mean, dispersion and correlation structure varying in depth. The general smooth structure is thereby disturbed by peaks and outliers so that robust procedures have to be applied for estimation. In terms of statistical modelling technology we have to tackle three different peculiarities of the data simultaneously, that is estimation of the correlation structure, local bandwidth selection and robust smoothing. To do so, existing routines are adapted and combined in new 'two stage' estimation procedures.

In this paper we review certain aspects around the Value-at-Risk, which is nowadays the industry benchmark risk measure. As a small quantile (usually 1%) Value-at-Risk is closely related to extreme value theory. We explain an estimation method based on extreme value theory. Since the variance of the estimated Value-at-Risk may depend on the dependence structure of the data, we investigate the extreme behaviour of some of the most prominent time series models in finance, continuous as well as discrete time models. We also determine optimal portfolios, when risk is measured by the Value-at-Risk. Again we use realistic models, moving away from the traditional Black-Scholes model to the class of Lévy processes. This paper is the contribution to a book by several authors on Extreme Value Theory, which will appear by CRC/Chapman and Hall.

Based on a reversible jump Markov Chain Monte Carlo (RJMCMC) algorithm which was developed by Fronk and Giudici (2000) to deal with model selection for Gaussian dags, we propose a new approach for the pure discrete case. Here, the main idea is to introduce latent variables which then allow to fall back on the already treated continuous case. This makes it also straightforward to tackle the mixed case, i.e. to deal simultaneously with continuous and discrete variables. The performance of the approach is investigated by means of a simulation study for different standard situations. In addition, a real data application is provided.

After a short introduction of the model, the missing mechanism and the method of inference some imputation procedures are introduced with special focus on the simulation experiment. Within this experiment, the simple additive model y = f(x) + e is assumed to have missing values in the independent variable according to MCAR. Besides the well-known complete case analysis, mean imputation plus random noise, a single imputation and two ways of nearest neighbor imputation are used. These methods are compared within a simulation experiment based on the average mean square error, variances and biases of hat{f}(x) at the knots.

Do reported reservation wages correspond to the concept of reservation wages that economists have? Using panel data on British unemployed I calculate reservation wages from a search model and compare these with reported reservation wages. It is shown that men's reported reservation wages are greater than what the model predicts, and that for women there is hardly a relation between the two variables.

The incidence of underweight amongst children under five in Western Africa has been increasing over the last decade (UNICEF, 2002). In Asia, where about two thirds of the world's underweight children live, the rate of underweight declined from about 36 per cent to some 29 per cent between 1990 and 2000. In sub-Saharan Africa, the absolute number of underweight children has increased and is now about 36 per cent. Using new data from Demographic and Health Surveys, I estimate the probability of underweight or a sample of West African children, controlling for selective survival.

Dempster-Shafer theory allows to construct belief functions from (precise) basic probability assignments. The present paper extends this idea substantially. By considering SETS of basic probability assignments, an appealing constructive approach to general interval probability (general imprecise probabilities) is achieved, which allows for a very flexible modelling of uncertain knowledge.

This paper studies Cox`s proportional hazards model under covariate measurement error. Nakamura`s (1990) methodology of corrected log-likelihood will be applied to the so called Breslow likelihood, which is, in the absence of measurement error, equivalent to partial likelihood. For a general error model with possibly heteroscedastic and non-normal additive measurement error, corrected estimators of the regression parameter as well as of the baseline hazard rate are obtained. The estimators proposed by Nakamura (1992), Kong, Huang and Li (1998) and Kong and Gu (1999) are reestablished in the special cases considered there. This sheds new light on these estimators and justifies them as exact corrected score estimators. Finally, the method will be extended to some variants of the Cox model.

Model selection in graphical models is still not fully investigated. The main difficulty lies in the search space of all possible models which grows more than exponentially with the number of variables involved. Here, genetic algorithms seem to be a reasonable strategy to find good fitting models for a given data set. In this paper, we adapt them to the problem of model search in graphical models and discuss their performance by conducting simulation studies.

The structural variant of a regression model with measurement error is characterized by the assumption of an underlying known distribution of the latent covariate. Several estimation methods, like regression calibration or structural quasi score estimation, take this distribution into account. In the case of a polynomial regression, which is studied here, structural quasi score takes the form of structural least squares (SLS). Usually the underlying latent distribution is assumed to be the normal distribution because then the estimation methods take a particularly simple form. SLS is consistent as long as this assumption is true. The purpose of the paper is to investigate the amount of bias that results from violations of the normality assumption for the covariate distribution. Deviations from normality are introduced by switching to a mixture of normal distributions. It turns out that the bias reacts only mildly to slight deviations from normality.

Proportional hazard models for survival data, even though popular and numerically handy, suffer from the restrictive assumption that covariate effects are constant over survival time. A number of tests have been proposed to check this assumption. This paper contributes to this area by employing local estimates allowing to fit hazard models with covariate effects smoothly varying with time. A formal test is derived to test the model with proportional hazards against the smooth general model as alternative. The test proves to possess omnibus power. Comparative simulations and two data examples accompany the presentation. Extensions are provided to multiple covariate settings, where the focus of interest is to decide which of the covariate effects vary with time.

We consider a Poisson model, where the mean depends on certain covariates in a log-linear way with unknown regression parameters. Some or all of the covariates are measured with errors. The covariates as well as the measurement errors are both jointly normally distributed, and the error covariance matrix is supposed to be known. Three consistent estimators of the parameters - the corrected score, a structural, and the quasi-score estimators - are compared to each other with regard to their relative (asymptotic) efficiencies. The paper extends an earlier result for a scalar covariate.

This paper considers an additive model y = f(x) + e when some observations on x are missing at random but corresponding observations on y are available. Especially for this model missing at random is an interesting case because of the fact that the complete case analysis is not expected to be suitable. A simulation study is reported and methods are compared based on superiority measures as the sample mean squared error, sample variance and estimated sample bias. In detail, complete case analysis, zero order regression plus random noise, single imputation and nearest neighbor imputation are discussed.

Nonignorable nonresponse is a common problem in bivariate or multivariate data. Here a selection model for bivariate normal distributed data (Y1 ; Y2) is proposed. The missingness of Y2 is supposed to depend on its own values. The model for missingness describes the probability of nonresponse in dependency of Y2 itself and it is chosen nonparametrically to allow exible patterns. We try to get a reasonable estimate for the expectation and especially for the variance of Y2 . Estimation is done by data augmentation and computation by common sampling methods.

This paper gives a detailed overview of the problem of missing data in parametric and nonparametric regression. Theoretical basics, properties as well as simulation results may help the reader to get familiar with the common problem of incomplete data sets. Of course, not all occurences can be discussed so this paper could be seen as an introduction to missing data within regression analysis and as an extension to the early paper of Little (1992).

We investigate the geographical and socioeconomic determinants of childhood undernutrition in Malawi, Tanzania and Zambia, three neighboring countries in Southern Africa using the 1992 Demographic and Health Surveys. We estimate models of undernutrition jointly for the three countries to explore regional patterns of undernutrition that transcend boundaries, while allowing for country-specific interactions. We use semiparametric models to flexibly model the effects of selected so-cioeconomic covariates and spatial effects. Our spatial analysis is based on a flexible geo-additive model using the district as the geographic unit of anal-ysis, which allows to separate smooth structured spatial effects from random effect. Inference is fully Bayesian and uses recent Markov chain Monte Carlo techniques. While the socioeconomic determinants generally confirm what is known in the literature, we find distinct residual spatial patterns that are not explained by the socioeconomic determinants. In particular, there appears to be a belt run-ning from Southern Tanzania to Northeastern Zambia which exhibits much worse undernutrition, even after controlling for socioeconomic effects. These effects do transcend borders between the countries, but to a varying degree. These findings have important implications for targeting policy as well as the search for left-out variables that might account for these residual spatial patterns.

A crucial task in modern genetic medicine is the understanding of complex genetic diseases. The main complicating features are that a combination of genetic and environmental risk factors is involved, and the phenotype of interest may be complex. Traditional statistical techniques based on lod-scores fail when the disease is no longer monogenic and the underlying disease transmission model is not defined. Different kinds of association tests have been proved to be an appropriate and powerful statistical tool to detect a candidate gene for a complex disorder. However, statistical techniques able to investigate direct and indirect influences among phenotypes, genotypes and environmental risk factors, are required to analyse the association structure of complex diseases. In this paper we propose graphical models as a natural tool to analyse the multifactorial structure of complex genetic diseases. An application of this model to primary hypertension data set is illustrated.

The Poisson regression model is often used as a first model for count data with covariates. Since this model is a GLM with canonical link, regression parameters can be easily fitted using standard software. However the model requires equidispersion, which might not be valid for the data set under consideration. There have been many models proposed in the literature to allow for overdispersion. One such model is the negative binomial regression model. In addition, score tests have been commonly used to detect overdispersion in the data. However these tests do not allow to quantify the effects of overdispersion. In this paper we propose easily interpretable discrepancy measures which allow to quantify the overdispersion effects when comparing a negative binomial regression to Poisson regression. We propose asymptotic $alpha$-level tests for testing the size of overdispersion effects in terms of the developed discrepancy measures. A graphical display of p-values curves can then be used to allow for an exact quantification of the overdispersion effects. This can lead to a validation of the Poisson regression or a discrimination of the Poisson regression with respect to the negative binomial regression. The proposed asymptotic tests are investigated in small samples using simulation and applied to two examples.

This paper discusses point estimation of the coefficients of polynomial measurement error (errors-in-variables) models. This includes functional and structural models. The connection between these models and total least squares (TLS) is also examined. A compendium of existing as well as new results is presented.

This contribution studies the Cox model under covariate measurement error. Methods proposed in the literature to adjust for measurement error are reviewed. The basic structural and functional approaches are discussed in some detail, important modifications and further developments are briefly sketched. Then the basic methods are compared in a simulation study.

Usual sequential testing procedures often are very sensitive against even small deviations from the `ideal model' underlying the hypotheses. This makes robust procedures highly desirable. To rely on a clearly defined optimality criterion, we incorporate robustness aspects directly into the formulation of the hypotheses considering the problem of sequentially testing between two interval probabilities (imprecise probabilities). We derive the basic form of the Kiefer-Weiss optimal testing procedure and show how it can be calculated by an easy-to-handle optimization problem. These results are based on the reinterpretation of our testing problem as the task to test between nonparametric composite hypotheses, which allows to adopt the framework of Pavlov (1991). From this we obtain a general result applicable to any interval probability field on a finite sample space, making the approach powerful far beyond robustness considerations, for instance for applications in artificial intelligence dealing with imprecise expert knowledge.

One important component of model selection using generalized linear models (GLM) is the choice of a link function. Approximate Bayes factors are used to assess the improvement in fit over a GLM with canonical link when a parametric link family is used. For this approximate Bayes factors are calculated using the approximations given in Raftery (1996), together with a reference set of prior distributions. This methodology can also be used to differentiate between different parametric link families, as well as allowing one to jointly select the link family and the independent variables. This involves comparing nonnested models. This is illustrated using parametric link families studied in Czado (1997) for two data sets involving binomial responses.

We present a nonparametric Bayesian method for fitting unsmooth and highly oscillating functions, which is based on a locally adaptive hierarchical extension of standard dynamic or state space models. The main idea is to introduce locally varying variances in the state equations and to add a further smoothness prior for this variance function. Estimation is fully Bayesian and carried out by recent MCMC techniques. The whole approach can be understood as an alternative to other nonparametric function estimators, such as local or penalized regression with variable bandwidth or smoothing parameter selection. Performance is illustrated with simulated data, including unsmooth examples constructed for wavelet shrinkage, and by an application to sales data. Although the approach is developed for classical Gaussian nonparametric regression, it can be extended to more complex regression problems.

Motivated by multivariate random recurrence equations we prove a new analogue of the Key Renewal Theorem for functionals of a Markov chain with compact state space in the spirit of Kesten. We simplify and modify Kesten's proof.

Order restricted effects of predictors can be represented in models by the monotonic transformation fitted by the pooled adjacent violators algorithm as described by T. Robertson et al. In the context of multivariate modelling, this paper aims to introduce next to additive monotonic models a multidimensional approach. The corresponding permutations test to assess significance for the predictors is described and some feeble points of the approach are discussed. We also introduce a procedure to improve the parsimony of the model by reducing the resulting level sets. The use of monotonic regression in connection with the threshold value estimation problematic is outlined and two similar approaches to assess it are discussed.

The AR-ARCH and AR-GARCH models, which allow for conditional heteroskedasticity and autoregression, reduce to random walk or white noise for some values of the parameters. We consider generalised versions of the AR-ARCH(1) and AR-GARCH(1,1) models, and, under mild assumptions, calculate the asymptotic distributions of pseudo-likelihood ratio statistics for testing hypotheses that reect these reductions. These hypotheses are of two kinds: the conditional volatility parameters may take their boundary values of zero, or the autoregressive component may take the form of a unit root process or not in fact be present. The limiting distributions of the resulting test statistics can be expressed in terms of functionals of Brownian motion related to the Dickey-Fuller statistic, together with independent chi-square components. The finite sample performances of the test statistics are assessed by simulations, and percentiles are tabulated. The results have applications in the analysis of financial time series and random coefficient models.

Varying-coefficient models provide a flexible framework for semi- and nonparametric generalized regression analysis. We present a fully Bayesian B-spline basis function approach with adaptive knot selection. For each of the unknown regression functions or varying coefficients, the number and location of knots and the B-spline coefficients are estimated simultaneously using reversible jump Markov chain Monte Carlo sampling. The overall procedure can therefore be viewed as a kind of Bayesian model averaging. Although Gaussian responses are covered by the general framework, the method is particularly useful for fundamentally non-Gaussian responses, where less alternatives are available. We illustrate the approach with a thorough application to two data sets analysed previously in the literature: the kyphosis data set with a binary response and survival data from the Veteran’s Administration lung cancer trial.

Generalized additive mixed models extend the common parametric predictor of generalized linear models by adding unknown smooth functions of different types of covariates as well as random effects. From a Bayesian viewpoint, all effects as well as smoothing parameters are random. Assigning appropriate priors, posterior inference can be based on Markov chain Monte Carlo techniques within a unified framework. Given observations on the response and on covariates, questions like the following arise: Can the additive structure be recovered? How well are unknown functions and effects estimated? Is it possible to discriminate between different types of random effects? The aim of this paper is to obtain some answers to such questions through a careful simulation study. Thereby, we focus on models for Gaussian and categorical responses based on smoothness priors as in Fahrmeir and Lang (2001). The result of the study provides valuable insight into the facilities and limitations of the models when applying them to real data.

We propose a new class of state space models for longitudinal discrete response data where the observation equation is specified in an additive form involving both deterministic and dynamic components. These models allow us to explicitly address the effects of trend, seasonal or other time-varying covariates while preserving the power of state space models in modeling dynamic pattern of data. We develop different Markov chain Monte Carlo algorithms to carry out statistical inference for models with binary and binomial responses. In a simulation experiment we investigate the mixing and convergence properties of these algorithms. In particular, we demonstrate that a joint state variable update is preferable over individual updates. In addition, different prior choices are studied. Finally, we illustrate the applicability of the proposed state space mixed models for longitudinal binomial response data in the analysis of the Tokyo rainfall data (Kitagawa 1987).

In a polynomial regression with measurement errors in the covariate, which is supposed to be normally distributed, one has (at least) three ways to estimate the unknown regression parameters: one can apply ordinary least squares (OLS) to the model without regard of the measurement error or one can correct for the measurement error, either by correcting the estimating equation (ALS) or by correcting the mean and variance functions of the dependent variable, which is done by conditioning on the observable, error ridden, counter part of the covariate (SLS). While OLS is biased the other two estimators are consistent. Their asymptotic covariance matrices can be compared to each other, in particular for the case of a small measurement error variance.

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In this paper binary state space mixed models of Czado and Song (2001) are applied to construct individual risk profiles based on a daily dairy of a migraine headache sufferer. These models allow for the modeling of a dynamic structure together with parametric covariate effects. Since the analysis is based on posterior inference using Markov Chain Monte Carlo (MCMC) methods, Bayesian model fit and model selection criteria are adapted to these binary state space mixed models. It is shown how they can be used to select an appropriate model, for which the probability of a headache today given the occurrence or nonoccurrence of a headache yesterday in dependency on weather conditions such as windchill and humidity can be estimated. This can provide the basis for pain management of such patients.

P-splines are an attractive approach for modelling nonlinear smooth effects of covariates within the generalized additive and varying coefficient models framework. In this paper we propose a Bayesian version for P-splines and generalize the approach for one dimensional curves to two dimensional surface fitting for modelling interactions between metrical covariates. A Bayesian approach to P-splines has the advantage of allowing for simultaneous estimation of smooth functions and smoothing parameters. Moreover, it can easily be extended to more complex formulations, for example to mixed models with random effects for serially or spatially correlated response. Additionally, the assumption of constant smoothing parameters can be replaced by allowing the smoothing parameters to be locally adaptive. This is particularly useful in situations with changing curvature of the underlying smooth function or where the function is highly oscillating. Inference is fully Bayesian and uses recent MCMC techniques for drawing random samples from the posterior. In a couple of simulation studies the performance of Bayesian P-splines is studied and compared to other approaches in the literature. We illustrate the approach by a complex application on rents for flats in Munich.

Generalized linear models (GLMs) and semiparametric extensions provide a flexible framework for analyzing the claims process in non-life insurance. Currently, most applications are still based on traditional GLMs, where covariate effects are modelled in form of a linear predictor. However, these models may already be too restrictive if nonlinear effects of metrical covariates are present. Moreover, although data are often collected within longer time periods and come from different geographical regions, effects of space and time are usually totally neglected. We provide a Bayesian semiparametric approach, which allows to simultaneously incorporate effects of space, time and further covariates within a joint model. The method is applied to analyze costs of hospital treatment and accommodation for a large data set from a German health insurance company.

When prior estimates of regression coefficients along with their stan¡ dard errors or their variance covariance matrix are available, they can be incorporated into the estimation procedure through minimax linear and mixed regression approaches. It is demonstrated that the mixed regres¡ sion approach provides more efficient estimators, at least asymptotically, in comparison to the minimax linear approach with respect to the criterion of variance covariance matrix.

Assuming the nonavailability of some observations and the availability of some stochastic linear constraints connecting the coefficients in a linear regression, the technique of mixed regression estimation is considered and a set of five unbiased estimators for the vector of coefficeints is presented. They are compared with respect to the criterion of variance covariance matrix and conditions are obtained for the superiority of one estimator over the other.

We have considered the estimation of coefficients in a linear regression model when some responses on the study variable are missing and some prior information in the form of lower and upper bounds for the average values of missing responses is available. Employing the mixed regression framework, we have presented five estimators for the vector of regression coefficients. Their exact as well as asymptotic properties are discussed and superiority of one estimator over the other is examined.

This paper deals with the application of the weighted mixed regression estimation of the coefficients in a linear model when some values of some of the regressors are missing. Taking the weight factor as an arbitrary scalar, the performance of weighted mixed regression estimator in relation to the conventional least squares and mixed regression estimators is analyzed and the choice of scalar is discussed. Then taking the weight factor as a specific matrix, a family of estimators is proposed and its performance properties under the criteria of bias vector and mean squared error matrix are analyzed.

The success of a newly founded company or small business depends on various initial risk factors or staring conditions, respectively, like e.g. the market the business aims for, the experience and the age of the founder, the preparation prior to the launch, the financial frame, the legal basis of the company and many others. These risk factors determine the chance of survival for the venture in the market. However, the effects of these risk factors often change with time. They may vanish or even increase with the time the company is in the market. In this paper we analyse the survival of 1123 newly founded companies in the state of Bavaria, Germany. Our focus is thereby primarily on the investigation of time-variation of the initial factors for success. The time-variation is thereby tackled within the framework of varying coefficient models, as introduced by Hastei and Tibshirani (1993, J.R.S.S. B.), where time modifies the effects of risk factors. An important issue in our analysis is the separation of risk factors which have time-varying effects from those which have time-constant effects. We make use of the Akaike criterion to separate these two types of factors.

We consider two consistent estimators for the parameters of the linear predictor in the Poisson regression model, where the covariate is measured with errors. The measurement errors are assumed to be normally distributed with known error variance sigma_u^2. The SQS estimator, based on a conditional mean-variance model, takes the distribution of the latent covariate into account, and this is here assumed to be a normal distribution. The CS estimator, based on a corrected score function, does not use the distribution of the latent covariate. Nevertheless, for small sigma_u^2, both estimators have identical asymptotic covariance matrices up to the order of sigma_u^2. We also compare the consistent estimators to the naive estimator, which is based on replacing the latent covariate with its (erroneously) measured counterpart. The naive estimator is biased, but has a smaller covariance matrix than the consistent estimators (at least up to the order of sigma_u^2.)

We estimate semiparametric regression models of chronic undernutrition (stunting) using the 1992 Demographic and Health Surveys (DHS) from Tanzania and Zambia. We focus particularly on the influence of the child's age, the mother's body mass index, and spatial influences on chronic undernutrition. Conventional parametric regression models are not flexible enough to cope with possibly nonlinear effects of the continuous covariates and cannot flexibly model spatial influences. We present a Bayesian semiparametric analysis of the effects of these two covariates on chronic undernutrition. Moreover, we investigate spatial determinants of undernutrition in these two countries. Compared to previous work with a simple fixed effects approach for the influence of provinces, we model small scale district specific effects using flexible spatial priors. Inference is fully Bayesian and uses recent Markov chain Monte Carlo techniques.

This article presents a modified Newton method for minimizing the Generalized Cross-Validation criterion, a commonly used smoothing parameter selection method in nonparametric regression. The method is applicable to higher dimensional problems such as additive and generalized additive models, and provides a computationally efficient alternative to full grid search in such cases. The implementation of the proposed method requires the estimation of a number of auxiliary quantities, and simple estimators are suggested. This article describes the methodology for local polynomial regression smoothing.

We consider online monitoring of sequentially arising data as e.g. met in clinical information systems. The general focus thereby is to detect breakpoints, i.e. timepoints where the measurement series suddenly changes the general level. The method suggested is based on local estimation. In particular, local linear smoothing is combined by ridging with local constant smoothing. The procedure is demonstrated by examples and compared with other available online monitoring routines.

We propose two approaches for the spatial analysis of cancer incidence data with additional information on the stage of the disease at time of diagnosis. The two formulations are extensions of commonly used models for multicategorical response data on an ordinal scale. We include spatial and age group effects in both formulations, which we estimate in a nonparametric smooth way. More specifically, we adopt a fully Bayesian approach based on Gaussian pairwise difference priors where additional smoothing parameters are treated as unknown as well. We apply our methods to data on cervical cancer in the former German Democratic Republic. The results suggest that there are large spatial differences in the stage-proportions, which indicates spatial variability with respect to the introduction and effectiveness of screening programs.

Semiparametrically structured models are defined as a class of models for which the predictors may contain parametric parts, additive parts of covariates with an unspecified functional form and interactions which are described as varying coefficients. In the case of an ordinal response the complexity of the predictor is determined by different sorts of effects. It is distinguished between global effects and category-specific effects where the latter allow that the effect varies across response categories. A general framework is developed in which global as well as category-specific effects may have unspecified functional form. The framework extends various existing methods of modeling ordinal responses. The Wilcoxon-Rogers notation is extended to incorporate smooth model parts and varying coefficient terms, the latter being important for the smooth specification of category-specific effects.

Generalized linear mixed models are a common tool in statistics which extends generalized linear models to situations where data are hierarchically clustered or correlated. In this article the simple but often inadequate restriction to a linear form of the predictor variables is dropped. A class of semiparametrically structured models is proposed in which the predictor decomposes into components that may be given by a parametric term, an additive form of unspecified smooth functions of covariates, varying-coefficient terms or terms which vary smoothly (or not) across the repetitions in a repeated measurement design. The class of models is explicitly designed as an extension of multivariate generalized mixed linear models such that ordinal responses may be treated within this framework. The modelling of smooth effects is based on basis functions like e.g. B-splines or radial basis functions. For the estimation of parameters a penalized marginal likelihood approach is proposed which may be based on integration techniques like Gauss-Hermite quadrature but may as well be used within the more recently developed nonparametric maximum likelihood approaches. For the maximization of the penalized marginal likelihood the EM-algorithm is adapted. Moreover, an adequate form of cross-validation is developed and shown to work satisfactorily. Various examples demonstrate the flexibility of the class of models.

This paper considers the problem of linear calibration and presents two estimators arising from a synthesis of classical and inverse calibration approaches. Their performance properties are analyzed employing the small error asymptotic theory. Using the criteria of bias and mean squared error, the proposed estimators along with the traditional classical and inverse calibration are compared. Finally, some remarks related to future work are placed.

This paper analyses the impact of the Hungarian unemployment insurance (UI) benefit system on the speed of exit from unemployment to regular employment. The duration analysis relies on unemployment spells from two inflow cohorts, which are administered under distinct UI rules. Thus, it exploits a natural experiment to identify disincentive effects. Kaplan-Meier estimates suggest that the benefit reform did not significantly change the transition rates. Moreover, a semi-parametric analysis cannot find remarkable disincentive effects but an entitlement effect. The hazards of men and women rise somewhat in the last two months before they run out of UI benefit.