Statistics 597A
Asymptotic Tools
Fall 2003
Lecture Notes
I'll post each day's handout in pdf format.
There will generally be one or two pages of overlap between consecutive
sets of notes due to the fact that topics usually begin in the middle of a
page. Therefore, if you are printing several days' notes, you should
omit the last page(s) for all but the last day (or you can simply print
the cumulative notes so far).
These notes are loosely based on the textbook by Erich Lehmann,
with various additions and modifications.
Cumulative notes so far (Topics 1-34)
- Tuesday, Sept. 2 (Topics 1-6)
- Tuesday, Sept. 9 (Topics 7-8)
- Thursday, Sept. 11 (Topics 9-10)
- Thursday, Sept. 18 (Topics 11-12)
- Tuesday, Sept. 23 (Topics 13-14)
- Tuesday, Sept. 30 (Topic 15)
- Thursday, Oct. 2 (Topics 16-17)
- Tuesday, Oct. 7 (Topics 18-19)
- Thursday, Oct. 16 (Topic 20)
- Tuesday, Oct. 21 (Topics 21-22)
- Thursday, Oct. 23 (Topics 23-26)
- Tuesday, Nov. 25 (Topic 27)
Topics covered so far:
- Limits
- Embedding Sequences
- Infinite Series
- Order Relations
- Continuity
- Distribution Functions
- Convergence in Probability
- Consistent Estimates of Mean
- Convergence in Law
- Extreme Order Statistics
- Uniform Convergence and the Dominated Convergence Theorem
- The Central Limit Theorem
- Taylor's Theorem and the Delta Method
- Central Limit Theorem for Dependent Sequences
- Multivariate Notions of Convergence
- Joint Distributions of Extreme Order Statistics
- The Multivariate Normal Distribution
- Sample Correlation Coefficient
- Uniform Order Statistics and Sample Quantiles
- Pearson's Chi-Square Statistic
- Characteristic Functions
- Power and Sample Size
- Asymptotic Relative Efficiency
- Asymptotic Power of Pearson's Chi-Square Test
- The Wilcoxon Rank-Sum Test
- Maximum Likelihood Estimation
- Asymptotic Normality of the MLE
- Efficient Estimation
- Fisher Information in the Multiparameter Case
- Efficient Estimation in the Multiparameter Case
- Wald, Score, and Likelihood Ratio Tests
- Statistical Functionals and V-statistics
- U-statistics
- Multisample U-statistics and Jointly Distributed U-statistics
R code seen in class
From time to time, I demonstrate some R programming techniques in
class. Below is posted the text of what I've done.
dhunter@stat.psu.edu