In this paper we investigate several tests for the hypothesis of a parametric form of the error distribution in the common linear and nonparametric regression model, which are based on empirical processes of residuals. It is well known that tests in this context are not asymptotically distribution-free and the parametric bootstrap is applied to deal with this problem. The performance of the resulting bootstrap test is investigated from an asymptotic point of view and by means of a simulation study. The results demonstrate that even for moderate sample sizes the parametric bootstrap provides a reliable and easy accessible solution to the problem of goodness-of-fit testing of assumptions regarding the error distribution in linear and nonparametric regression models.

In the classical linear regression model the problem of testing for symmetry of the error distribution is considered. The test statistic is a functional of the difference between the two empirical distribution functions of the estimated residuals and their counterparts with opposite signs. The weak convergence of the difference process to a Gaussian process is established. The covariance structure of this process depends heavily on the density of the error distribution, and for this reason the performance of a symmetric wild bootstrap procedure is discussed in asymptotic theory and by means of a simulation study.

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may AbstractThe aim of this paper is to show that existing estimators for the error distribution in nonparametric regression models can be improved when additional information about the distribution is included by the empirical likelihood method. The weak convergence of the resulting new estimator to a Gaussian process is shown and the performance is investigated by comparison of asymptotic mean squared errors and by means of a simulation study. As a by-product of our proofs we obtain stochastic expansions for smooth linear estimators based on residuals from the nonparametric regression model.

We present a new approach to handle dependencies within the general framework of case control designs in genetic epidemiology. These dependencies arise from relatives being present in the sample thus violating iid assumptions. The theoretical background for data analysis becomes more complex by allowing for this modification. A theorem is proven in a general context characterizing the joint asymptotic distribution of the entries in the associated contingency tables under the null hypothesis of independence of phenotype and genotype at the observed locus. As relevant for applications in genetic epidemiology, the asymptotic distribution of several tests can be derived from our result. In particular, we consider tests on equality of allele frequencies and odds ratios. A simulation study reveals the finite sample behaviour of these test statistics. Our results can also be applied to more general settings in medicine or natural science.