دانلود کتاب آمار ریاضی – جلد دوم

This textbook represents our view of what a second course in mathematical statistics for graduate students with a good mathematics background should be. The mathematics background needed includes linear algebra, matrix theory and advanced calculus, but not measure theory. Probability at the level of, for instance, Grimmett and Stirzaker’s Probability and Random Processes, is also needed. Appendix D1 in combination with Appendices A and B in Volume I give the probability that is needed. However, the treatment is abridged with few proofs. This Volume II of the second edition presents what we think are some of the most important statistical concepts, methods, and tools developed since the first edition. Topics included are: asymptotic efficiency in semiparametric models, semiparametric maximum likelihood estimation, finite sample size optimality including Lehmann-Scheff´e theory, survival analysis including Cox regression, prediction, classification, methods of inference based on sieve models, model and variable selection, Monte Carlo methods such as the bootstrap and Markov Chain Monte Carlo, nonparametric curve estimation, and machine learning including support vector machines and classification and regression trees (CART). The basic asymptotic tools developed or presented, in part in the text and in part in appendices, are weak convergence for random processes, empirical process theory, and the functional delta method. With the tools and concepts developed in this second volume students will be ready for advanced research in modern statistics.