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Adaptive bootstrap tests and its competitors in the c-sample scale problem

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  • Herbert Buning
  • Michael Rietz

Abstract

This paper deals with a study of different types of tests for the two-sided c-sample scale problem. We consider the classical parametric test of Bartlett [M.S. Bartlett, Properties of sufficiency and statistical tests, Proc. R. Stat. Soc. Ser. A. 160 (1937), pp. 268-282] several nonparametric tests, especially the test of Fligner and Killeen [M.A. Fligner and T.J. Killeen, Distribution-free two-sample tests for scale, J. Amer. Statist. Assoc. 71 (1976), pp. 210-213], the test of Levene [H. Levene, Robust tests for equality of variances, in Contribution to Probability and Statistics, I. Olkin, ed., Stanford University Press, Palo Alto, 1960, pp. 278-292] and a robust version of it introduced by Brown and Forsythe [M.B. Brown and A.B. Forsythe, Robust tests for the equality of variances, J. Amer. Statist. Assoc. 69 (1974), pp. 364-367] as well as two adaptive tests proposed by Buning [H. Buning, Adaptive tests for the c-sample location problem - the case of two-sided alternatives, Comm. Statist.Theory Methods. 25 (1996), pp. 1569-1582] and Buning [H. Buning, An adaptive test for the two sample scale problem, Nr. 2003/10, Diskussionsbeitrage des Fachbereich Wirtschaftswissenschaft der Freien Universitat Berlin, Volkswirtschaftliche Reihe, 2003]. which are based on the principle of Hogg [R.V. Hogg, Adaptive robust procedures. A partial review and some suggestions for future applications and theory, J. Amer. Statist. Assoc. 69 (1974), pp. 909-927]. For all the tests we use Bootstrap sampling strategies, too. We compare via Monte Carlo Methods all the tests by investigating level α and power β of the tests for distributions with different strength of tailweight and skewness and for various sample sizes. It turns out that the test of Fligner and Killeen in combination with the bootstrap is the best one among all tests considered.

Suggested Citation

  • Herbert Buning & Michael Rietz, 2008. "Adaptive bootstrap tests and its competitors in the c-sample scale problem," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(8), pages 853-866.
    • Handle: RePEc:taf:japsta:v:35:y:2008:i:8:p:853-866
    DOI: 10.1080/02664760802124257
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    References listed on IDEAS

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    1. Lim, Tjen-Sien & Loh, Wei-Yin, 1996. "A comparison of tests of equality of variances," Computational Statistics & Data Analysis, Elsevier, vol. 22(3), pages 287-301, July.
    2. Thorpe, David P. & Holland, Burt, 2000. "Some multiple comparison procedures for variances from non-normal populations," Computational Statistics & Data Analysis, Elsevier, vol. 35(2), pages 171-199, December.
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