Asymptotic Expansions for General Statistical Models PDF Download
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Author: Johann Pfanzagl
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 522
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Book Description
Author: Johann Pfanzagl
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 522
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Book Description
Author: O. E. Barndorff-Nielsen
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 272
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Book Description
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.
Author: Ib M. Skovgaard
Publisher: IMS
ISBN: 9780940600201
Category : Mathematics
Languages : en
Pages : 182
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Book Description
Author: Vladimir E. Bening
Publisher: Walter de Gruyter
ISBN: 3110935996
Category : Mathematics
Languages : en
Pages : 305
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Book Description
The series is devoted to the publication of high-level monographs and surveys which cover the whole spectrum of probability and statistics. The books of the series are addressed to both experts and advanced students.
Author: Nancy Reid
Publisher: World Scientific
ISBN: 9813207876
Category : Mathematics
Languages : en
Pages : 364
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Book Description
This book showcases the innovative research of Professor Skovgaard, by providing in one place a selection of his most important and influential papers. Introductions by colleagues set in context the highlights, key achievements, and impact, of each work. This book provides a survey of the field of asymptotic theory and inference as it was being pushed forward during an exceptionally fruitful time. It provides students and researchers with an overview of many aspects of the field.
Author: Rabi Bhattacharya
Publisher: Springer
ISBN: 1493940325
Category : Mathematics
Languages : en
Pages : 386
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Book Description
This graduate-level textbook is primarily aimed at graduate students of statistics, mathematics, science, and engineering who have had an undergraduate course in statistics, an upper division course in analysis, and some acquaintance with measure theoretic probability. It provides a rigorous presentation of the core of mathematical statistics. Part I of this book constitutes a one-semester course on basic parametric mathematical statistics. Part II deals with the large sample theory of statistics - parametric and nonparametric, and its contents may be covered in one semester as well. Part III provides brief accounts of a number of topics of current interest for practitioners and other disciplines whose work involves statistical methods.
Author:
Publisher: John Wiley & Sons
ISBN: 0471743917
Category : Mathematics
Languages : en
Pages : 722
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Book Description
ENCYCLOPEDIA OF STATISTICAL SCIENCES
Author: D.R. Cox
Publisher: CRC Press
ISBN: 9780412494406
Category : Mathematics
Languages : en
Pages : 376
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Book Description
Likelihood and its many associated concepts are of central importance in statistical theory and applications. The theory of likelihood and of likelihood-like objects (pseudo-likelihoods) has undergone extensive and important developments over the past 10 to 15 years, in particular as regards higher order asymptotics. This book provides an account of this field, which is still vigorously expanding. Conditioning and ancillarity underlie the p*-formula, a key formula for the conditional density of the maximum likelihood estimator, given an ancillary statistic. Various types of pseudo-likelihood are discussed, including profile and partial likelihoods. Special emphasis is given to modified profile likelihood and modified directed likelihood, and their intimate connection with the p*-formula. Among the other concepts and tools employed are sufficiency, parameter orthogonality, invariance, stochastic expansions and saddlepoint approximations. Brief reviews are given of the most important properties of exponential and transformation models and these types of model are used as test-beds for the general asymptotic theory. A final chapter briefly discusses a number of more general issues, including prediction and randomization theory. The emphasis is on ideas and methods, and detailed mathematical developments are largely omitted. There are numerous notes and exercises, many indicating substantial further results.
Author: Christopher G. Small
Publisher: CRC Press
ISBN: 1420011022
Category : Mathematics
Languages : en
Pages : 359
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Book Description
Asymptotic methods provide important tools for approximating and analysing functions that arise in probability and statistics. Moreover, the conclusions of asymptotic analysis often supplement the conclusions obtained by numerical methods. Providing a broad toolkit of analytical methods, Expansions and Asymptotics for Statistics shows how asymptoti
Author:
Publisher: American Mathematical Soc.
ISBN: 0821848216
Category : Mathematics
Languages : en
Pages : 243
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Book Description
This volume contains translations of papers that originally appeared in the Japanese journal Sugaku. The papers range over a variety of topics in probability theory, statistics, and applications. This volume is suitable for graduate students and research mathematicians interested in probability and statistics.
