Statistics: Asymptotic Tools

 Contents:

Limits; Embedding Sequences; Infinite Series; Order Relations; Continuity; Distribution Functions; Convergence in Probability;

Regression estimators, sample mean for non-iid sequences;

Convergence in Law; Asymptotic distributions, extreme order statistics;

Uniform convergence;

Central Limit Theorem;

Taylor's theorem and the delta method;

Independent but not identically distributed;

Dependent sequences;

Multivariate notions of convergence;

Joint distributions of extreme order statistics; Th

e multivariate normal distribution;

Sample correlation coefficient;

Change of variables; Quantiles;

Pearson's chi-square statistic;

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;

Nuisance parameters; Wald, score, and likelihood ratio tests;

Statistical functionals and V-statistics;

U-statistics;

Multisample U-statistics and jointly distributed U-statistics;

Bootstrapping.

                                                                                                     << Back