Asymptotic Techniques for Use in Statistics (Monographs on Statistics and Applied Probability): 31 (Chapman & Hall/CRC Monographs on Statistics and Applied Probability) - Softcover

Barndorff-Nielsen, O.E.; Cox, D.R.

 
9780412314001: Asymptotic Techniques for Use in Statistics (Monographs on Statistics and Applied Probability): 31 (Chapman & Hall/CRC Monographs on Statistics and Applied Probability)
Softcover
ISBN 10: 0412314002 ISBN 13: 9780412314001
Verlag: Chapman and Hall/CRC, 1989

Inhaltsangabe

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.

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Reseña del editor

The use in statistical theory of approximate arguments based on such methods as local linearization (the delta method) and approxi­ mate normality has a long history. Such ideas play at least three roles. First they may give simple approximate answers to distributional problems where an exact solution is known in principle but difficult to implement. The second role is to yield higher-order expansions from which the accuracy of simple approximations may be assessed and where necessary improved. Thirdly the systematic development of a theoretical approach to statistical inference that will apply to quite general families of statistical models demands an asymptotic formulation, as far as possible one that will recover 'exact' results where these are available. The approximate arguments are developed by supposing that some defining quantity, often a sample size but more generally an amount of information, becomes large: it must be stressed that this is a technical device for generating approximations whose adequacy always needs assessing, rather than a 'physical' limiting notion. Of the three roles outlined above, the first two are quite close to the traditional roles of asymptotic expansions in applied mathematics and much ofthe very extensive literature on the asymptotic expansion of integrals and of the special functions of mathematical physics is quite directly relevant, although the recasting of these methods into a probability mould is quite often enlightening.

Reseña del editor

This book sets out in detail mathematical techniques valuable for giving useful approximate solutions to a wide range of problems in statistical theory and method 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, there are roughly 100 further results and exercises many of which outline recent research results. This book should be of interest to advanced students of statistics; research statisticians.

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Verlag
Chapman and Hall/CRC
Erscheinungsdatum
1989
Sprache
Englisch
ISBN 10 
0412314002
ISBN 13 
9780412314001
Einband
Tapa blanda
Auflage
1
Anzahl der Seiten
240
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Verantwortliche Person
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