Asymptotic Techniques for Use in Statistics

9780412314001

0412314002

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 whichoutline 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.