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This book puts its weight on theoretical issues related to finite mixture models. It shows that a good applicant, is an applicant who understands the issues behind each statistical method. This book is intended for applicants whose interests include some understanding of the procedures they are using, while they do not have to read the technical derivations.
At the same time, many researchers find most theories and techniques necessary for the development of various statistical methods, without chasing after one set of research papers, after another. Even though the book emphasizes the theory, it provides accessible numerical tools for data analysis. Readers with strength in developing statistical software, may find it useful.
Table des matières
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.
