We consider the problem of estimating the noise variance in homoscedastic nonparametric regression models. For low dimensional covariates "t"  is an element of   R-super-"d", "d"=1, 2, difference-based estimators have been investigated in a series of papers. For a given length of such an estimator, difference schemes which minimize the asymptotic mean-squared error can be computed for "d"=1 and "d"=2. However, from numerical studies it is known that for finite sample sizes the performance of these estimators may be deficient owing to a large finite sample bias. We provide theoretical support for these findings. In particular, we show that with increasing dimension "d" this becomes more drastic. If "d"⩾4, these estimators even fail to be consistent. A different class of estimators is discussed which allow better control of the bias and remain consistent when "d"⩾4. These estimators are compared numerically with kernel-type estimators (which are asymptotically efficient), and some guidance is given about when their use becomes necessary. Copyright 2005 Royal Statistical Society.

An essential problem in planning clinical non-inferiority or equivalence studies is the specification of the 'irrelevant difference' (irrelevance margin; delta). This quantifies the amount of non-inferiority or difference, respectively, between a new test therapy and an established standard treatment which is to be considered as tolerable. In the past, most recommendations and guidelines for clinical non-inferiority and equivalence studies contained only general statements and formulations concerning the specification of delta. The current unsatisfactory situation was the reason for performing a systematic review of published clinical non-inferiority and equivalence studies. It was the aim to gain an overview on the irrelevance margins used in such studies, and on reasons for choosing the particular margins. For the sake of comparability, the irrelevance margins were converted into standardized differences and odds ratios. Overall, there were 332 non-inferiority or equivalence trials obtained by means of an extensive literature search. The results of the systematic review show that current requirements on the choice of delta and the reality of recent clinical non-inferiority and equivalence trials differ substantially. In about one half of the trials a difference of 0.5 standard deviations or more was regarded as 'irrelevant' explicitly or implicitly. Estimates of standard-placebo differences formed the basis of the irrelevance margin in less than every tenth trial. Reasons for this very low proportion might be (1) the possibly resulting very small irrelevance margins, and (2) unsolved problems of the requirements themselves. Overall, it seems that a more global definition of 'irrelevance' might be warranted.

Semiparametric models to describe the functional relationship between k groups of observations are broadly applied in statistical analysis, ranging from nonparametric ANOVA to proportional hazard (ph) rate models in survival analysis. In this paper we deal with the empirical assessment of the validity of such a model, which will be denoted as a ''structural relationship model''. To this end Hadamard differentiability of a suitable goodness-of-fit measure in the k-sample case is proved. This yields asymptotic limit laws which are applied to construct tests for various semiparametric models, including the Cox ph model. Two types of asymptotics are obtained, first when the hypothesis of the semiparametric model under investigation holds true, and second for the case when a fixed alternative is present. The latter result can be used to validate the presence of a semiparametric model instead of simply checking the null hypothesis ''the model holds true''. Finally, various bootstrap approximations are numerically investigated and a data example is analyzed. r

This article presents a short review on guidelines for dissolution profile testing, particularly focusing on the recommendations regarding statistical methods for assessing profile similarity. In this context, the guidelines on in vitroh vivo correlations and on granting biowaivers are outlined briefly. The comparison of two dissolution profiles can be performed in different ways. There are many model-dependent and model-independent procedures suggested in the methodical literature. Current guidelines primarily recommend the application of a method based upon the f2 statistic as a measure of the similarity of two dissolution curves, though this procedure has often been criticized recently. The goal of this article is to give a survey of the current guidelines, including a description and discussion of the recommended methods for data analysis.

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