Statistics 597A
Asymptotic Tools
Fall 2002
Lecture Notes
- Topics 1-6
- Limits
- Embedding Sequences
- Infinite Series
- Order Relations
- Continuity
- Distribution Functions
- Topics 7-10
- Convergence in Probability
- Regression estimators, sample mean for non-iid sequences
- Convergence in Law
- Asymptotic distributions, extreme order statistics
- Topics 11-13
- Uniform convergence
- Central Limit Theorem, Part I: iid case
- Taylor's theorem and the delta method
- Topic 14
- CLT, Part II: Independent but not identically distributed
- Topic 15
- CLT, Part III: Dependent sequences
- Topic 16
- Multivariate notions of convergence
- Topics 17-18
- Joint distributions of extreme order statistics
- The multivariate normal distribution
- Topic 19
- Sample correlation coefficient
- Topics 20-22
- Change of variables
- Quantiles
- Pearson's chi-square statistic
- Topics 23-24
- Power and sample size
- Asymptotic relative efficiency
- Topics 25-26
- Asymptotic power of Pearson's chi-square test
- The Wilcoxon Rank-Sum Test
- Topics 27-28
- Maximum likelihood estimation
- Asymptotic normality of the MLE
- Topics 29-33
- Efficient estimation
- Fisher information in the multiparameter case
- Efficient estimation in the multiparameter case
- Nuisance parameters
- Wald, score, and likelihood ratio tests
- Topics 34-35
- Statistical functionals and V-statistics
- U-statistics
- Topics 36-37
- Multisample U-statistics and jointly distributed U-statistics
- Bootstrapping
dhunter@stat.psu.edu