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Statistics: Asymptotic Tools

Author: David Hunter
Url: http://www.stat.psu.edu/~dhunter/asymp/fall2002/lectures/
Format: Pdf
Category: Statistics
Pages: 100
Clicks: 2884

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; The 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.

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