Asymptotic null distribution of the modified likelihood ratio test for homogeneity in finite mixture models
| Autor: | Kwok Fai Lam, Tony Siu Tung Wong, Victoria X. Zhao |
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| Rok vydání: | 2018 |
| Předmět: |
Statistics and Probability
Generalized linear model 010504 meteorology & atmospheric sciences Applied Mathematics Homogeneity (statistics) Linear model Asymptotic distribution 01 natural sciences 010104 statistics & probability Computational Mathematics Computational Theory and Mathematics Likelihood-ratio test Statistical inference Test statistic Null distribution Applied mathematics 0101 mathematics 0105 earth and related environmental sciences Mathematics |
| Zdroj: | Computational Statistics & Data Analysis. 127:248-257 |
| ISSN: | 0167-9473 |
| DOI: | 10.1016/j.csda.2018.05.010 |
| Popis: | Likelihood-based methods play a central role in statistical inference for parametric models. Among these, the modified likelihood ratio test is preferred in testing for homogeneity in finite mixture models. The test statistic is related to the maximum of a quadratic function under general regularity conditions. Re-parameterization is shown to have overcome the difficulty when linear independence is not satisfied. Models with parameter constraints are also considered. The asymptotic null distribution of the test statistic is shown to have a chi-bar-squared distribution in both constrained and unconstrained cases. We extend the result to linear models and demonstrate that the chi-bar-squared distribution is also applicable. The general asymptotic result provides a much simpler testing procedure with an exact form of the asymptotic distribution compared to re-sampling approach in the literature. It also offers accurate p -value as shown in simulation. The results are checked by extensive simulation and are supplemented by a breast cancer data example. |
| Databáze: | OpenAIRE |
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