### 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.