Abstract
Summary Testing for homogeneity in finite mixture models has been investigated by many researchers. The asymptotic null distribution of the likelihood ratio test (LRT) is very complex and difficult to use in practice. We propose a modified LRT for homogeneity in finite mixture models with a general parametric kernel distribution family. The modified LRT has a χ-type of null limiting distribution and is asymptotically most powerful under local alternatives. Simulations show that it performs better than competing tests. They also reveal that the limiting distribution with some adjustment can satisfactorily approximate the quantiles of the test statistic, even for moderate sample sizes.
Keywords
Homogeneity (statistics)MathematicsLikelihood-ratio testQuantileAsymptotic distributionParametric statisticsStatisticsScore testApplied mathematicsNull distributionLimitingStatisticNull hypothesisParametric modelTest statisticRatio testKernel density estimationStatistical hypothesis testingEngineering
Affiliated Institutions
Related Publications
Testing for a Finite Mixture Model with Two Components
Summary We consider a finite mixture model with k components and a kernel distribution from a general one-parameter family. The problem of testing the hypothesis k=2 versusk⩾3 i...
The likelihood ratio test for homogeneity in finite mixture models
Abstract The authors study the asymptotic behaviour of the likelihood ratio statistic for testing homogeneity in the finite mixture models of a general parametric distribution f...
Inference on the Order of a Normal Mixture
Finite normal mixture models are used in a wide range of applications. Hypothesis testing on the order of the normal mixture is an important yet unsolved problem. Existing proce...
On Bootstrapping the Likelihood Ratio Test Stastistic for the Number of Components in a Normal Mixture
An important but difficult problem in practice is assessing the number of components g in a mixture. An obvious way of proceeding is to use the likelihood ratio test statistic λ...
Likelihood Ratio Tests for Model Selection and Non-Nested Hypotheses
In this paper, we develop a classical approach to model selection. Using the Kullback-Leibler Information Criterion to measure the closeness of a model to the truth, we propose ...
Publication Info
- Year
- 2001
- Type
- article
- Volume
- 63
- Issue
- 1
- Pages
- 19-29
- Citations
- 221
- Access
- Closed
External Links
Social Impact
Altmetric
PlumX Metrics
Social media, news, blog, policy document mentions
Citation Metrics
221
OpenAlex
Cite This
Hanfeng Chen,
Jiahua Chen,
John D. Kalbfleisch
(2001).
A Modified Likelihood Ratio Test for Homogeneity in Finite Mixture Models.
Journal of the Royal Statistical Society Series B (Statistical Methodology)
, 63
(1)
, 19-29.
https://doi.org/10.1111/1467-9868.00273
Identifiers
- DOI
- 10.1111/1467-9868.00273