Discussion Papers 2017

CIRJE-F-1044	"Testing the Order of Multivariate Normal Mixture Models"
Author Name	Kasahara, Hiroyuki and Katsumi Shimotsu
Date	March 2017
Full Paper	PDF file
Remarks

Abstract
Testing the number of components in multivariate normal mixture models is a long-standing challenge. This paper develops a likelihood-based test of the null hypothesis of M0 components against the alternative hypothesis of M0 + 1 components. We derive a local quadratic approximation of the likelihood ratio statistic in terms of the polynomials of the parameters. Based on this quadratic approximation, we propose an EM test of the null hypothesis of M0 components against the alternative hypothesis of M0 + 1 components, and derive the asymptotic distribution of the proposed test statistic. The simulations show that the proposed test has good finite sample size and power properties.
Keywords: asymptotic distribution; EM test; likelihood ratio test; local MLE; multivariate normal mixture models; number of components

Abstract

Testing the number of components in multivariate normal mixture models is a long-standing challenge. This paper develops a likelihood-based test of the null hypothesis of M0 components against the alternative hypothesis of M0 + 1 components. We derive a local quadratic approximation of the likelihood ratio statistic in terms of the polynomials of the parameters. Based on this quadratic approximation, we propose an EM test of the null hypothesis of M0 components against the alternative hypothesis of M0 + 1 components, and derive the asymptotic distribution of the proposed test statistic. The simulations show that the proposed test has good finite sample size and power properties.

Keywords: asymptotic distribution; EM test; likelihood ratio test; local MLE; multivariate normal mixture models; number of components