A Course in Large Sample Theory

ISBN-13: 9781138445765 / Angielski / Twarda / 2017

Ferguson, Thomas S.

Opis

This is a first year graduate text on large sample theory in statistics. Nearly all topics are covered in their multivariate settings. The text falls into four parts and includes many examples. In the first part, basic probabilistic notions are treated.

Spis treści

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

O autorze

Thomas S. Ferguson