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) |
|---|---|
| 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 |
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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.
In: Statistics and Probability Letters, Vol. 71, No. 3, 01.03.2005, p. 225-235.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 -