Statistical Inference Under Mixture Models

1. Introduction to mixture models.- 2. Nonparametric MLE and its consistency.- 3. Maximum likelihood estimation under finite mixture models.- 4. Estimation under finite normal mixture models.- 5. Consistent estimation under finite Gamma mixture.- 6. Geometric properties of nonparametric MLE and numerical solutions.- 7. EM-algorithm.- 8. Rate of convergence.- 9. Test of homogeneity.- 10. Likelihood ratio test for homogeneity.- 11. Modified likelihood ratio test.- 12. Modified likelihood ratio test for higher order.- 13 EM-test for homogeneity.- 14 EM-test for higher order.- 15 EM-test for univariate finite Gaussian mixture models.- 16 Order selection of the finite mixture models.- 17 A few key probability theory results employed.- References.

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• Probabilidade e Estatística

EM-algorithm;EM-test;Hypothesis test;Homogeneity;Likelihood ratio test;Maximum likelihood estimation;Mixture model;Modified likelihood;Nonparametric MLE;Optimal rate of convergence;Penalized MLE