In this paper we study statistical inference for certain inverse problems. We go beyond mere estimation purposes and review and develop the construction of confidence intervals and confidence bands in some inverse problems, including deconvolution and the backward heat equation. Further, we...

In this article we highlight the main differences of available methods for the analysis of regression functions that are probably additive separable. We first discuss definition and interpretation of the most common estimators in practice. This is done by explaining the different ideas of...

The determination of toxicokinetic parameters is an essential component in the risk assessment of potential harmful chemicals. It’s a first step to analyse the processes which are involved in the development of DNA adducts and might therefore lead to the development of cancer. The complete...

Necessary and sufficient conditions for the equality of ordinary least squares and generalized least squares estimators in the linear regression model with firstorder spatial error processes are given.

In this paper we derive asymptotic x2-tests for general linear hypotheses on variance components using repeated variance components models. In two examples, the two-way nested classification model and the two-way crossed classification model with interaction, we explicitly investigate the...

This report extends the technique of testing single variance components with generalized fixed-level tests in situations when nuisance parameters make exact testing impossible to the more general way of testing hypotheses on linear forms of variance components. An extension of the definition of...

In many fields of applications, test statistics are obtained by combining estimates from several experiments, studies or centres of a multicentre trial. The commonly used test procedure to judge the evidence of a common overall effect can result in a considerable overestimation of the...

In geostatistics, spatial data will be analysed that often come from irregularly distributed sampling locations. Interest is in modelling the data, i.e. estimating distributional parameters and then to predict the phenomenon under study at unobserved sites within the corresponding sampling...

The minimum number of misclassifications achievable with affine hyper_ planes on a given set of labeled points is a key quantity in both statistics and computational learning theory. However, determining this quantity exactly is essentially NP_hard_ cf_ Höfgen, Simon and van Horn (1995.) Hence,...