Adaptive Tests for the c-Sample Location Problem

Herbert Büning ()
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Herbert Büning: Freie Universität Berlin

A chapter in Statistical Inference, Econometric Analysis and Matrix Algebra, 2009, pp 3-17 from Springer

Abstract: Abstract This paper deals with the concept of adaptive tests and with an application to the c-sample location problem. Parametric tests like the ANOVA F-tests are based on the assumption of normality of the data which is often violated in practice. In general, the practising statistician has no clear idea of the underlying distribution of his data. Thus, an adaptive test should be applied which takes into account the given data set. We use the concept of Hogg [21], i.e. to classify, at first, the unknown distribution function with respect to two measures, one for skewness and one for tailweight, and then, at the second stage, to select an appropriate test for that classified type of distribution. It will be shown that under certain conditions such a two-staged adaptive test maintains the level. Meanwhile, there are a lot of proposals for adaptive tests in the literature in various statistical hypotheses settings. It turns out that all these adaptive tests are very efficient over a broad class of distributions, symmetric and asymmetric ones.

Keywords: Adaptive Scheme; Underlying Distribution; Adaptive Test; Selector Statistic; Adaptive Procedure (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-7908-2121-5_1

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DOI: 10.1007/978-3-7908-2121-5_1

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