### Abstract

Determining the number of components in a mixture distribution is of interest to researchers in many areas. In this paper, we investigate the statistical properties of a likelihood ratio test proposed by Lo et al. (Biometrika 88 (2001) 767) for determining the number of components in a normal mixture with unequal variances. We discuss the dependence of the rate of convergence of the likelihood ratio statistic to its limiting distribution on the choice of restrictions imposed on the component variances to deal with the problem of unboundedness of the likelihood. We compare the test procedure to the parametric bootstrap method and posterior predictive checks, a Bayesian model checking procedure.

Original language | English (US) |
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Pages (from-to) | 225-235 |

Number of pages | 11 |

Journal | Statistics and Probability Letters |

Volume | 71 |

Issue number | 3 |

DOIs | |

State | Published - Mar 1 2005 |

### Fingerprint

### Keywords

- Bootstrap test
- Likelihood ratio test
- Normal mixture
- Posterior predictive checks

### ASJC Scopus subject areas

- Statistics, Probability and Uncertainty
- Statistics and Probability

### Cite this

**Likelihood ratio tests of the number of components in a normal mixture with unequal variances.** / Lo, Yungtai.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Likelihood ratio tests of the number of components in a normal mixture with unequal variances

AU - Lo, Yungtai

PY - 2005/3/1

Y1 - 2005/3/1

N2 - Determining the number of components in a mixture distribution is of interest to researchers in many areas. In this paper, we investigate the statistical properties of a likelihood ratio test proposed by Lo et al. (Biometrika 88 (2001) 767) for determining the number of components in a normal mixture with unequal variances. We discuss the dependence of the rate of convergence of the likelihood ratio statistic to its limiting distribution on the choice of restrictions imposed on the component variances to deal with the problem of unboundedness of the likelihood. We compare the test procedure to the parametric bootstrap method and posterior predictive checks, a Bayesian model checking procedure.

AB - Determining the number of components in a mixture distribution is of interest to researchers in many areas. In this paper, we investigate the statistical properties of a likelihood ratio test proposed by Lo et al. (Biometrika 88 (2001) 767) for determining the number of components in a normal mixture with unequal variances. We discuss the dependence of the rate of convergence of the likelihood ratio statistic to its limiting distribution on the choice of restrictions imposed on the component variances to deal with the problem of unboundedness of the likelihood. We compare the test procedure to the parametric bootstrap method and posterior predictive checks, a Bayesian model checking procedure.

KW - Bootstrap test

KW - Likelihood ratio test

KW - Normal mixture

KW - Posterior predictive checks

UR - http://www.scopus.com/inward/record.url?scp=14044250133&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=14044250133&partnerID=8YFLogxK

U2 - 10.1016/j.spl.2004.11.007

DO - 10.1016/j.spl.2004.11.007

M3 - Article

AN - SCOPUS:14044250133

VL - 71

SP - 225

EP - 235

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

IS - 3

ER -