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基本説明
Aims to bring together those ideas useful especially in monograph statistics and to present them, including the most recent work, in a form where the general concepts involved can be easily understood and applied.
Full Description
This book sets out in detail mathematical techniques valuable for giving useful approximate solutions to a wide range of problems in statistical theory and methods as well as in applied probability. The emphasis throughout is on the relatively simple general concepts involved and on their illustration by a wide range of examples, chosen to be of intrinsic interest. The precise mathematical theorems with their associated, rather formidable technical conditions are given as appendices, but the emphasis in the body of the text is on applications. The first four chapters deal with univariate problems, where the key ideas are seen in their simplest, yet widely useful, form. The last three chapters deal with the corresponding multivariate problems. The notation, especially the use of tensor methods, has been chosen to emphasize the parallel with one dimensional results. In addition to the examples, which are an intrinsic part of the text, there are roughly 100 further results and exercises, many of which outline recent research results. The book is aimed at a number of different types of reader, including advanced statistics and probability students and research workers in these and related fields.
Contents
Preliminary notions.- Some basic limiting procedures.- Asymptotic expansions.- Edgeworth and allied expansions.- Miscellany on multivariate distributions.- Multivariate asymptotic expansions.- Expansions for conditional distributions.- Postscript.
