Theory and Methods of Statistics

ISBN-13: 9780128024409 / Angielski / Miękka / 2016 / 544 str.

Bhattacharya, P.K. Burman, Prabir

Opis

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

Recenzje

"There will always be a need for a small number of mathematical statisticians, and this book would be a viable choice for training those people...In addition to its use as a textbook, this volume would make a good reference on the theory behind many standard methods."--MAA Reviews

Spis treści

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

O autorze

P.K. Bhattacharya has more than 30 years of experience teaching a broad spectrum of undergraduate and graduate courses in Statistics at Indian Statistical Institute, the University of Arizona, the University of California, Davis, and as a visiting professor at the University of Minnesota and MIT. He has supervised PhD students and has done professional consulting. He has authored more than 40 scientific papers in various areas of Statistics in leading statistical journals and has served on the editorial boards of Annals of Statistics and Sankhya. Prabir Burman has more than 30 years of teaching experience at University of California, Davis, Rutgers University, and Singapore National University. He has taught a wide variety of courses in Statistics courses at undergraduate and graduate levels, and he supervises PhD students in Statistics. He has also performed professional consulting. The author of more than 40 scientific publications in statistics and scientific journals, he is currently on the editorial board of the Journal of Multivariate Analysis, Statistics and Probability Letters, and ISRN Journal of Probability and Statistics.