Approximate Distributions Of Order Statistics: With Applications To Nonparametric Statistics (springer Series In Statistics)

This book is designed as a unified and mathematically rigorous treatment of some recent developments of the asymptotic distribution theory of order statistics (including the extreme order statistics) that are relevant for statistical theory and its applications. Particular emphasis is placed on results concern­ ing the accuracy oflimit theorems, on higher order approximations, and other approximations in quite a general sense. Contrary to the classical limit theorems that primarily concern the weak convergence of distribution functions, our main results will be formulated in terms of the variational and the Hellinger distance. These results will form the proper springboard for the investigation of parametric approximations of nonparametric models of joint distributions of order statistics. The approxi­ mating models include normal as well as extreme value models. Several applications will show the usefulness of this approach. Other recent developments in statistics like nonparametric curve estima­ tion and the bootstrap method will be studied as far as order statistics are concerned. 1n connection with this, graphical methods will, to some extent, be explored. This book is designed as a unified and mathematically rigorous treatment of some recent developments of the asymptotic distribution theory of order statistics (including the extreme order statistics) which are relevant for statistical theory and its applications. Particular emphasis is placed on results concerning the accuracy of limit theorems, on higher order approximations and other approximations in quite a general sense. Contrary to the classical limit theorems, that primarily concern the weak convergence of distribution functions, our main results will be formulated in terms of the variational and the Hellinger distance. These results will form the proper springboard for the investigation of parametric approximations of nonparametric models of joint distributions of order statistics. The approximating models include normal as well as extreme value models. Several applications will show the usefulness of this approach. This book is intended for students and research workers in probability and statistics, and practitioners involved in applications of mathematical results conderning order statistics and extremes. The knowledge of calculus and topics that are taught in introductory probability and statistic courses are necessary for the understanding of this book. Front Matter....Pages i-xii Introduction....Pages 1-8 Front Matter....Pages 9-9 Distribution Functions, Densities, and Representations....Pages 11-63 Multivariate Order Statistics....Pages 64-82 Inequalities and the Concept of Expansions....Pages 83-104 Front Matter....Pages 105-105 Approximations to Distributions of Central Order Statistics....Pages 107-150 Approximations to Distributions of Extremes....Pages 151-205 Other Important Approximations....Pages 206-228 Approximations in the Multivariate Case....Pages 229-239 Front Matter....Pages 241-241 Evaluating the Quantile and Density Quantile Function....Pages 243-271 Extreme Value Models....Pages 272-291 Approximate Sufficiency of Sparse Order Statistics....Pages 292-317 Back Matter....Pages 318-355 can you get me a copy from this article on my email torkzidan@gmail.com thank you