Theory and Methods of Statistics

Theory and Methods of Statistics covers essential topics for advanced graduate students and professional research statisticians. This comprehensive resource covers many important areas in one manageable volume, including core subjects such as probability theory, mathematical statistics, and linear models, and various special topics, including nonparametrics, curve estimation, multivariate analysis, time series, and resampling. The book presents subjects such as "maximum likelihood and sufficiency," and is written with an intuitive, heuristic approach to build reader comprehension. It also includes many probability inequalities that are not only useful in the context of this text, but also as a resource for investigating convergence of statistical procedures.

Codifies foundational information in many core areas of statistics into a comprehensive and definitive resourceServes as an excellent text for select master’s and PhD programs, as well as a professional referenceIntegrates numerous examples to illustrate advanced conceptsIncludes many probability inequalities useful for investigating convergence of statistical procedures

1. Probability Theory 2. Some Common Probability Distributions 3. Infinite Sequence of Random Variables and Their Convergence Properties 4. Basic Concepts of Statistical Inference and a Decision Theoretic Approach 5. Point Estimation in Parametric Models 6. Hypotheses Testing in Parametric Models 7. Asymptotic Properties of Likelihood Based Methods 8. Ranks, Empirical Distribution Functions and Quantiles 9. Nonparametric Curve Estimation 10. Statistical Functionals 11. Inference in Linear Models 12. Multivariate Analysis 13. Resampling: Jackknife and Bootstrap 14. Time Series

Appendix A. Some Results from Advanced Calculus B. Some Inequalities C. Stieltjes Integration D.  Convergence in Law E. Contiguity F. Weak Convergence