Hiroyuki Kasahara, Katsumi Shimotsu
arXiv 8 Feb 2019 · Mathematics — Statistics Theory · 1 citations (OpenAlex)
arXiv:1902.02920 · PDF · DOI · OpenAlex · Extracted main text
Finite mixtures of multivariate normal distributions have been widely used in empirical applications in diverse fields such as statistical genetics and statistical finance. Testing the number of components in multivariate normal mixture models is a long-standing challenge even in the most important case of testing homogeneity. This paper develops likelihood-based tests of the null hypothesis of $M_0$ components against the alternative hypothesis of $M_0 + 1$ components for a general $M_0 \geq 1$. For heteroscedastic normal mixtures, we propose an EM test and derive the asymptotic distribution of the EM test statistic. For homoscedastic normal mixtures, we derive the asymptotic distribution of the likelihood ratio test statistic. We also derive the asymptotic distribution of the likelihood ratio test statistic and EM test statistic under local alternatives and show the validity of parametric bootstrap. The simulations show that the proposed test has good finite sample size and power properties.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Chen, J. and Li, P (2009) Hypothesis Test for Normal Mixture Models: The EM Approach | 0.928 | 4 | 3 | 100% |
| 2 | Kasahara, H. and Shimotsu, K (2015) Testing the Number of Components in Normal Mixture Regression Models self | 0.843 | 4 | 3 | 75% |
| 3 | Chen, H. and Chen, J (2003) Tests for Homogeneity in Normal Mixtures in the Presence of a Structural Parameter | 0.811 | 4 | 2 | 100% |
| 4 | Chen, J. and Tan, X (2009) Inference for Multivariate Normal Mixtures | 0.794 | 6 | 3 | 50% |
| 5 | Chen, J., Li, P., and Fu, Y (2012) Inference on the Order of a Normal Mixture | 0.737 | 3 | 2 | 100% |
| 6 | Liu, X. and Shao, Y (2003) Asymptotics for Likelihood Ratio Tests under Loss of Identifiability | 0.644 | 4 | 2 | 50% |
| 7 | Dempster, A. P., Laird, N. M., and Rubin, D. B (1977) Maximum Likelihood from Incomplete Data via EM Algorithm (with Discussion) | 0.511 | 2 | 2 | 50% |
| 8 | Li, P. and Chen, J (2010) Testing the Order of a Finite Mixture | 0.511 | 2 | 2 | 50% |
| 9 | Azas, J.-M., Gassiat, É., and Mercadier, C (2009) The Likelihood Ratio Test for General Mixture Models with or without Structural Parameter | 0.511 | 2 | 1 | 100% |
| 10 | Dacunha-Castelle, D. and Gassiat, E (1999) Testing the Order of a Model using Locally Conic Parametrization: Population Mixtures and Stationary ARMA Processes | 0.511 | 2 | 1 | 100% |
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