A Course in Large Sample Theory (Hardcover)

Preface viiPart 1 Basic Probability 11 Modes of Convergence 32 Partial Converses to Theorem 1 83 Convergence in Law 134 Laws of Large Numbers 195 Central Limit Theorems 26Part 2 Basic Statistical Large Sample Theory 376 Slutsky Theorems 397 Functions of the Sample Moments 448 The Sample Correlation Coefficient 519 Pearson’s Chi-Square 5610 Asymptotic Power of the Pearson Chi-Square Test 61Part 3 Special Topics 6711 Stationary m-Dependent Sequences 6912 Some Rank Statistics 7513 Asymptotic Distribution of Sample Quantiles 8714 Asymptotic Theory of Extreme Order Statistics 9415 Asymptotic Joint Distributions of Extrema 101Part 4 Efficient Estimation and Testing 10516 A Uniform Strong Law of Large Numbers 10717 Strong Consistency of Maximum-Likelihood Estimates 11218 Asymptotic Normality of the Maximum-LikelihoodEstimate 11919 The Cram6r-Rao Lower Bound 12620 Asymptotic Efficiency 13321 Asymptotic Normality of Posterior Distributions 14022 Asymptotic Distribution of the Likelihood RatioTest Statistic 14423 Minimum Chi-Square Estimates 15124 General Chi-Square Tests 163Appendix: Solutions to the exercises 172References 236Index