Theory and Methods of Statistics

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.

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