A Course in Large Sample Theory is presented in four parts. The first treats basic probabilistic notions, the second features the basic statistical tools for expanding the theory, the third contains special topics as applications of the general theory, and the fourth covers more standard statistical topics. Nearly all topics are covered in their multivariate setting.The book is intended as a first year graduate course in large sample theory for statisticians. It has been used by graduate students in statistics, biostatistics, mathematics, and related fields. Throughout the book there are many examples and exercises with solutions. It is an ideal text for self study.

part 1|35 pages

Basic Probability Theory

chapter 1|5 pages

Modes of Convergence

chapter 2|5 pages

Partial Converses to Theorem 1

chapter 3|6 pages

Convergence in Law

chapter 4|7 pages

4 Laws of Large Numbers

chapter 5|10 pages

5 Central Limit Theorems

part 2|30 pages

Basic Statistical Large Sample Theory

chapter 6|5 pages

Slutsky Theorems

chapter 7|7 pages

Functions of the Sample Moments

chapter 8|5 pages

The Sample Correlation Coefficient

chapter 9|5 pages

Pearson’s Chi-Square

part 3|38 pages

Special Topics

chapter 11|6 pages

Stationary m-Dependent Sequences

chapter 12|12 pages

Some Rank Statistics

chapter 15|4 pages

Asymptotic Joint Distributions of Extrema

part 4|67 pages

Efficient Estimation and Testing

chapter 16|5 pages

A Uniform Strong Law of Large Numbers

chapter 19|7 pages

The Cramér-Rao Lower Bound

chapter 20|7 pages

Asymptotic Efficiency

chapter 23|12 pages

Minimum Chi-Square Estimates

chapter 24|9 pages

24 General Chi-Square Tests