Distribution-free tests for polynomial regression based on simplicial depth

JOURNAL OF MULTIVARIATE ANALYSIS

卷:100

Article

Wellmann, Robin¹  Harmand, Peter²  Mueller, Christine H.¹ 

[1] Univ Kassel, Dept Math, D-34109 Kassel, Germany

[2] Carl von Ossietzky Univ Oldenburg, D-2900 Oldenburg, Germany

关键词: Distribution-free tests;    Simplicial depth;    Regression depth;    Polynomial regression;    Degenerated U-statistic;    Spectral decomposition;    Outlier robustness;   

DOI  :  10.1016/j.jmva.2008.06.009

来源: Elsevier

【 摘 要 】

A general approach for developing distribution-free tests for general linear models based on simplicial depth is presented. In most relevant cases, the test statistic is a degenerated U-statistic so that the spectral decomposition of the conditional expectation of the kernel function is needed to derive the asymptotic distribution. A general formula for this conditional expectation is derived. Then it is shown how this general formula can be specified for polynomial regression. Based on the specified form, the spectral decomposition and thus the asymptotic distribution is derived for polynomial regression of arbitrary degree. The power of the new test is compared via simulation with other tests. An application on cubic regression demonstrates the applicability of the new tests and in particular their outlier robustness. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free