Open Access
December 2009 Multi-sample Rényi test statistics
Tomáš Hobza, Isabel Molina, Domingo Morales
Braz. J. Probab. Stat. 23(2): 196-215 (December 2009). DOI: 10.1214/08-BJPS008


This paper focuses on testing composite hypotheses about parameters of s independent samples of different sizes. With this purpose, it introduces test statistics based on the family of Rényi divergences between likelihoods. The asymptotic distributions of the proposed test statistics and of the likelihood ratio statistic are derived under standard regularity assumptions. An application to test the homogeneity of variances in data from families belonging to different populations is described and, under this setup, a simulation experiment compares the small sample performance of the likelihood ratio test and some members of the Rényi family of tests. The experiment indicates that some of the Rényi tests perform better under null hypothesis.


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Tomáš Hobza. Isabel Molina. Domingo Morales. "Multi-sample Rényi test statistics." Braz. J. Probab. Stat. 23 (2) 196 - 215, December 2009.


Published: December 2009
First available in Project Euclid: 26 October 2009

zbMATH: 1298.62035
MathSciNet: MR2575433
Digital Object Identifier: 10.1214/08-BJPS008

Keywords: divergence statistics , Homogeneity of variances , Rényi divergence , testing composite hypotheses

Rights: Copyright © 2009 Brazilian Statistical Association

Vol.23 • No. 2 • December 2009
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