Power of the likelihood ratio test for models of DNA base substitution

Abstract

The goal of this work is to study the properties of the likelihood ratio (LR) tests comparing base substitution models. These are the most widely used hypothesis tests. With mild regularity conditions, we show that the asymptotic distribution of the LR statistic test, under the alternative hypothesis, is a non-central chi-square distribution. The asymptotic normal distribution of the LR test is proved when the sequence length S goes to infinity. We also propose a consistent estimator for the non-centrality parameter D. Through asymptotic theory and based on this consistent estimator for D, we propose a low computational cost estimator for the power of the LR test. The methodology is applied to 17 different gene sequences of the ECP–EDN family in primates.

Keywords:

• phylogenetic inference
• Monte Carlo simulation
• evolutionary model
• maximum-likelihood function
• hypothesis test
• power of the test
• asymptotic distribution

Acknowledgements

G.B. Cybis was supported by CNPq-Brazil. S.R.C. Lopes research was partially supported by CNPq-Brazil, by CAPES-Brazil, by CNPq-INCT em Matemática and also by Pronex Probabilidade e Processos Estocásticos - E-26/170.008/2008 -APQ1. H.P. Pinheiro research was partially supported by CNPq-Brazil and by CAPES-Brazil. The authors thank two anonymous referees and the editor for their valuable comments and suggestions that improved the final version of the manuscript.