Additional Exercises for the book
"A Course in Large Sample Theory"
by Thomas S. Ferguson
Chapman & Hall, 1996.
Part 1: Basic Probability Theory.
1. Modes of Convergence. 5 exercises
2. Partial Converses. 7 exercises
3. Convergence in Law. 5 exercises
4. Laws of Large Numbers. 3 exercises
5. Central Limit Theorems. 12 exercises
Part 2: Basic Statistical Large Sample Theory
6. Slutsky Theorems. 6 exercises
7. Functions of the Sample Moments. 10 exercises
8. The Sample Correlation Coefficient. 4 exercises
9. Pearson's Chi-Square. 6 exercises
10. Asymptotic Power of the Pearson Chi-Square Test. 3 exercises
Part 3: Special Topics.
11. Stationary m-dependent Sequences. 6 exercises
12. Some Rank Statistics. 6 exercises
13. Asymptotic Distribution of Sample Quantiles. 5 exercises
14. Asymptotic Theory of Extreme Order Statistics. 6 exercises
15. Asymptotic Joint Distributions of Extrema. 4 exercises
Part 4: Efficient Estimation and Testing.
16. A Uniform Strong Law of Large Numbers.
17. Strong Consistency of the Maximum Likelihood Estimates. 4 exercises
18. Asymptotic Normality of the MLE. 6 exercises
19. The Cramer-Rao Lower Bound. 5 exercises
20. Asymptotic Efficiency. 6 exercises
21. Asymptotic Normality of Posterior Distributions. 3 exercises
22. Asymptotic Distribution of the Likelihood Ratio Test Statistic. 6 exercises
23. Minimum Chi-Square Estimates. 2 exercises
24. General Chi-Square Tests. 7 exercises
Errata
Errors and misprints in PDF.
Please let me know if you find any additional misprints or corrections.
Send e-mail to tom@math.ucla.edu.