A Course in Large Sample Theory

A Course in Large Sample Theory
Chapman & Hall, 1996.Table of Contents
Part 1: Basic Probability Theory.
1. Modes of Convergence.
2. Partial Converses.
3. Convergence in Law.
4. Laws of Large Numbers.
5. Central Limit Theorems.
Part 2: Basic Statistical Large Sample Theory
6. Slutsky Theorems.
7. Functions of the Sample Moments.
8. The Sample Correlation Coefficient.
9. Pearson's Chi-Square.
10. Asymptotic Power of the Pearson Chi-Square Test.
Part 3: Special Topics.
11. Stationary m-dependent Sequences.
12. Some Rank Statistics.
13. Asymptotic Distribution of Sample Quantiles.
14. Asymptotic Theory of Extreme Order Statistics.
15. Asymptotic Joint Distributions of Extrema.
Part 4: Efficient Estimation and Testing.
16. A Uniform Strong Law of Large Numbers.
17. Strong Consistency of the Maximum Likelihood Estimates.
18. Asymptotic Normality of the MLE.
19. The Cramer-Rao Lower Bound.
20. Asymptotic Efficiency.
21. Asymptotic Normality of Posterior Distributions.
22. Asymptotic Distribution of the Likelihood Ratio Test Statistic.
23. Minimum Chi-Square Estimates.
24. General Chi-Square Tests