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Full Description
This book is a unique compendium of core topics in the Statistics Ph.D. program, as well as covering the latest statistical theory, graduate probability and simulation techniques. The Complete Guide to Statistical Theory, Simulation and Probability: A Bridge to the Future gives an elaborate treatment of standard statistics topics such as parametric inference, basic theory of linear models, large sample theory, as well as more advanced topics such as robust estimation, density estimation, bootstrap, multiple testing, and the latest breakthrough developments such as the LASSO and thresholding and regularization. It also gives self-contained treatments of standard graduate probability and major Monte Carlo techniques, including MCMC. As such, this book can be used as an all-purpose text in the statistics Ph.D. programs, as well as a unique research reference.
The book provides 918 exercises, and an additional 98 exercises at the end of the book. The book also has a complete and comprehensive synopsis of real analysis, calculus, linear algebra and matrix theory as an invaluable source of consultation for students, instructors, and researchers.
Contents
Preface.- Chapter 1 Graduate Probability.- Chapter 2 Writing Models for Data.- Chapter 3 Exponential Families as a Unifier in Inference.- Chapter 4 The Problems of Inference: A Nontechnical First Glimpse.- Chapter 5 Decision Theory: Basic Concepts.- Chapter 6 Decision Theory: Basic Concepts.- Chapter 7 Bayes, Empirical Bayes and Shrinkage Estimates.- Chapter 8 Testing of Hypotheses and Confidence Regions.- Chapter 9 Asymptotic Approximations and Practical Asymptotic Tools.- Chapter 10 Least Squares Theory and Linear Models.- Chapter 11 Chi-square Tests.- Chapter 12 Empirical Processes and the Kolmogorov-Smirnov Tests.- Chapter 13 Density Estimation.- Chapter 14 Robust Estimates.- Chapter 15 Bootstrap, Jackknife and Permutation Tests.- Chapter 16 Simulation and the EM Algorithm.- Chapter 17 Markov Chain Monte Carlo.- Chapter 18 Epilogue: Metamorphosis of Statistics?.- Chapter 19 Sample Midterms.- Chapter 20 Appendix.- Index.
