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Statistics: Asymptotic Tools



Description 
Contents: Limits; Embedding Sequences; Infinite Series; Order Relations; Continuity; Distribution Functions; Convergence in Probability; Regression estimators, sample mean for noniid 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 chisquare statistic; Power and sample size; Asymptotic relative efficiency;
Asymptotic power of Pearson's; chisquare test; The Wilcoxon RankSum 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 Vstatistics; Ustatistics; Multisample Ustatistics and jointly distributed Ustatistics; Bootstrapping. 

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