Brazilian Journal of Probability and Statistics

Multi-sample Rényi test statistics

Tomáš Hobza, Isabel Molina, and Domingo Morales

Full-text: Open access

Abstract

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.

Article information

Source
Braz. J. Probab. Stat. Volume 23, Number 2 (2009), 196-215.

Dates
First available in Project Euclid: 26 October 2009

Permanent link to this document
https://projecteuclid.org/euclid.bjps/1256562758

Digital Object Identifier
doi:10.1214/08-BJPS008

Mathematical Reviews number (MathSciNet)
MR2575433

Keywords
Rényi divergence divergence statistics testing composite hypotheses homogeneity of variances

Citation

Hobza, Tomáš; Molina, Isabel; Morales, Domingo. Multi-sample Rényi test statistics. Braz. J. Probab. Stat. 23 (2009), no. 2, 196--215. doi:10.1214/08-BJPS008. https://projecteuclid.org/euclid.bjps/1256562758.


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