Statistics 597A
Asymptotic Tools
Fall 2002

Schedule of Topics

The following list of topics refers to my lecture notes.
  1. Limits
  2. Embedding Sequences
  3. Infinite Series
  4. Order Relations
  5. Continuity
  6. Distribution Functions
  7. Convergence in Probability
  8. Regression estimators, sample mean for non-iid sequences
  9. Convergence in Law
  10. Asymptotic distributions, extreme order statistics
  11. Uniform convergence
  12. Central Limit Theorem, Part I: iid case
  13. Taylor's theorem and the delta method
  14. CLT, Part II: Independent but not identically distributed
  15. CLT, Part III: Dependent sequences
  16. Multivariate notions of convergence
  17. Joint distributions of extreme order statistics
  18. The multivariate normal distribution
  19. Sample correlation coefficient
  20. Change of variables
  21. Quantiles
  22. Pearson's chi-square statistic
  23. Power and sample size
  24. Asymptotic relative efficiency
  25. Asymptotic power of Pearson's chi-square test
  26. The Wilcoxon Rank-Sum Test
  27. Maximum likelihood estimation
  28. Asymptotic normality of the MLE
  29. Efficient estimation
  30. Fisher information in the multiparameter case
  31. Efficient estimation in the multiparameter case
  32. Nuisance parameters
  33. Wald, score, and likelihood ratio tests
  34. Statistical functionals and V-statistics
  35. U-statistics
  36. Multisample U-statistics and jointly distributed U-statistics
  37. Bootstrapping
Below is a day-by-day summary of the topics we've covered:

Week 1 Tuesday
August 27		 Topics 1, 2, part of 3 up to power series
Thursday
August 29		 Rest of topic 3, topics 4, 5, 6
Week 2 Tuesday
September 3		 Topics 7 and part of 8 up to stationary and m-dependent sequences
Thursday
September 5		 Rest of topic 8 and most of topic 9 up to bounded in probability sequences
Week 3 Tuesday
September 10		 Rest of topic 9; Topics 10 and 11
R code seen in class
Thursday
September 12		 Topic 12
Week 4 Tuesday
September 17		 Topic 13, first part of Topic 14 up to the Lindeberg-Feller theorem
Thursday
September 19		 Rest of Topic 14
R code seen in class
Week 5 Tuesday
September 24		 Topic 15
Thursday
September 26		 Discussion of Lindeberg and Lyapunov conditions, upcoming test questions
Start of topic 16
Week 6 Tuesday
October 1		 Test over Topics 1-15
Thursday
October 3		 Finish Topic 16
Week 7 Tuesday
October 8		 Topic 17
Thursday
October 10		 Topic 18
Mathematica seen in class; R code seen in class
Week 8 Tuesday
October 15		 No class; fall break.
Thursday
October 17		 Topic 19
Mathematica seen in class
Week 9 Tuesday
October 22		 Topics 20 and 21
Thursday
October 24		 Topic 22
Week 10 Tuesday
October 29		 Start of Topic 23, through end of Theorem 23.1
Thursday
October 31		 Rest of Topic 23 and first part of Topic 24, through the middle of the Wilcoxon signed rank example
Week 11 Tuesday
November 5		 Finish Topic 24, start 25 (through proof of Lemma 25.1)
Thursday
November 7		 Finish Topics 25 and 26
Week 12 Tuesday
November 12		 Topic 27
Thursday
November 14		 Topic 28
Week 13 Tuesday
November 19		 Topic 29
Nov. 20Wednesday evening exam over Topics 16-26, 7:00pm
Thursday
November 21		 Topics 30 and 31, most of 32
Week 14 Tuesday
November 26		 Finish Topic 32, start 33
Thursday
November 28		 No class; Thanksgiving
Week 15 Tuesday
December 3		 Finish Topic 33, start 34
R code seen in class
Thursday
December 5		 Finish Topic 34, start 35
Week 16 Tuesday
December 10		 Finish Topics 35 and 36
Thursday
December 12		 Topic 37
Week 17 Final exam The final is scheduled for Friday, Dec. 20 from 4:40-6:30 pm.
However, we can decide on an alternate time if everyone agrees.


dhunter@stat.psu.edu