3. The Limiting Distribution of the EM Test of the Order of a Finite Mixture

  1. Kerrie L. Mengersen3,
  2. Christian P. Robert4 and
  3. D. Michael Titterington5
  1. Jiahua Chen1 and
  2. Pengfei Li2

Published Online: 24 APR 2011

DOI: 10.1002/9781119995678.ch3

Mixtures: Estimation and Applications

Mixtures: Estimation and Applications

How to Cite

Chen, J. and Li, P. (2011) The Limiting Distribution of the EM Test of the Order of a Finite Mixture, in Mixtures: Estimation and Applications (eds K. L. Mengersen, C. P. Robert and D. M. Titterington), John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9781119995678.ch3

Editor Information

  1. 3

    School of Mathematical Sciences, Queensland University of Technology, Australia

  2. 4

    Université Paris-Dauphine, CEREMADE, Paris, France

  3. 5

    University of Glasgow, Glasgow, UK

Author Information

  1. 1

    Department of Statistics University of British Columbia Vancouver, Canada

  2. 2

    Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Canada

Publication History

  1. Published Online: 24 APR 2011
  2. Published Print: 15 APR 2011

ISBN Information

Print ISBN: 9781119993896

Online ISBN: 9781119995678



  • limiting distribution of EM test - of the order of a finite mixture;
  • nonregularity of finite mixture models - statisticians meeting challenges, effective and easy-to-use methods;
  • modified likelihood ratio test (MLRT);
  • ideas in EM tests - tracing back to MLRT;
  • studying asymptotic behaviour - of a new inference method, focus of its development;
  • method and theory of EM test;
  • definition of EM test statistic - EM test statistic, constructed iteratively;
  • limiting distribution of EM test statistic;
  • proof of main result - involving a few major intermediate conclusions;
  • notion of partial EM iteration - new technique, expanding EM test statistic, origin in Chen et al. (2001)


This chapter contains sections titled:

  • Introduction

  • The method and theory of the EM test

  • Proofs

  • Discussion

  • References