Description
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 resource
- Serves as an excellent text for select master’s and PhD programs, as well as a professional reference
- Integrates numerous examples to illustrate advanced concepts
- Includes many probability inequalities useful for investigating convergence of statistical procedures
Table of Contents
1. Probability Theory2. Some Common Probability Distributions3. Infinite Sequence of Random Variables and Their Convergence Properties4. Basic Concepts of Statistical Inference and a Decision Theoretic Approach5. Point Estimation in Parametric Models6. Hypotheses Testing in Parametric Models7. Asymptotic Properties of Likelihood Based Methods8. Ranks, Empirical Distribution Functions and Quantiles9. Nonparametric Curve Estimation10. Statistical Functionals11. Inference in Linear Models12. Multivariate Analysis13. Resampling: Jackknife and Bootstrap14. Time Series
AppendixA. Some Results from Advanced CalculusB. Some InequalitiesC. Stieltjes IntegrationD. Convergence in LawE. ContiguityF. Weak Convergence
