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Likelihood Methods in Statistics : Oxford Statistical Science Series - Thomas A. Severini

Likelihood Methods in Statistics

Oxford Statistical Science Series

Hardcover Published: 1st December 2000
ISBN: 9780198506508
Number Of Pages: 392

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This book provides an introduction to the modern theory of likelihood-based statistical inference. This theory is characterized by several important features. One is the recognition that it is desirable to condition on relevant ancillary statistics. Another is that probability approximations are based on saddlepoint and closely related approximations that generally have very high accuracy. A third aspect is that, for models with nuisance parameters, inference is often based on marginal or conditional likelihoods, or approximations to these likelihoods. These methods have been shown often to yield substantial improvements over classical methods. The book also provide an up-to-date account of recent results in the field, which has been undergoing rapid development.

Industry Reviews

"This book presents an excellent overview of modern likelihood methods. The presentation is clear and readable enough to be of considerable use to intermediate level graduate students, but is complete and up-to-date enough to act as an excellent first reference for beginning researchers in the
field. . . . Moreover, there are excellent discussions of important references as well as numerous exercises. . . . The field of likelihood asymptotics has been undergoing an increasingly rapid development over the last two decades, and this book provides an excellent and detailed account of where
the field is, where it came from and perhaps even a bit about where it is going." -- Mathematical Reviews

Some basic conceptsp. 1
Introductionp. 1
Exponential family modelsp. 4
Transformation modelsp. 7
Cumulantsp. 11
Sufficiencyp. 16
Ancillary statisticsp. 19
Normal distribution theoryp. 22
Discussion and referencesp. 23
Exercisesp. 24
Large-sample approximationsp. 27
Introductionp. 27
Central limit theoremp. 28
Edgeworth series approximationsp. 31
Saddlepoint approximation of densitiesp. 37
Approximation of integrals and sumsp. 40
Saddlepoint approximations for distribution functionsp. 46
Saddlepoint approximations for lattice variablesp. 49
Saddlepoint approximations for multivariate distributionsp. 53
Stochastic asymptotic expansionsp. 54
Approximation of conditional distributionsp. 58
Laplace approximationsp. 66
Discussion and referencesp. 68
Exercisesp. 69
Likelihoodp. 73
Introductionp. 73
Some properties of the likelihood functionp. 75
The likelihood principlep. 77
Regular modelsp. 80
Log-likelihood derivativesp. 85
Informationp. 88
Methods of inferencep. 96
Discussion and referencesp. 100
Exercisesp. 102
First-order asymptotic theoryp. 105
Introductionp. 105
Maximum likelihood estimatesp. 105
The likelihood ratio statisticp. 113
The score and Wald statisticsp. 120
Confidence regionsp. 123
The profile likelihood functionp. 126
Nonregular modelsp. 129
Discussion and referencesp. 133
Exercisesp. 134
Higher-order asymptotic theoryp. 138
Introductionp. 138
Some preliminary resultsp. 138
Maximum likelihood estimatesp. 141
Likelihood ratio statisticp. 154
Saddlepoint approximationsp. 163
Discussion and referencesp. 171
Exercisesp. 172
Asymptotic theory and conditional inferencep. 175
Introductionp. 175
Log-likelihood derivativesp. 176
Conditional distribution of maximum likelihood estimatesp. 183
Stable inferencep. 196
Approximation of the conditional modelp. 204
Approximate ancillarityp. 209
Approximation of sample space derivativesp. 218
Discussion and referencesp. 234
Exercisesp. 235
The signed likelihood ratio statisticp. 238
Introductionp. 238
Normalizing transformationsp. 239
One-parameter modelsp. 241
Scalar parameter of interest in the presence of a nuisance parameterp. 248
Approximations to R*p. 261
Discussion and referencesp. 274
Exercisesp. 275
Likelihood functions for a parameter of interestp. 278
Introductionp. 278
Conditional likelihood functionsp. 279
Marginal likelihood functionsp. 298
Integrated likelihood functionsp. 306
Inference based on a pseudo-likelihood functionp. 309
Discussion and referencesp. 319
Exercisesp. 320
The modified profile likelihood functionp. 323
Introductionp. 323
Profile likelihoodp. 323
Modified profile likelihoodp. 327
Calculation of the modified profile likelihood without an explicit nuisance paramterp. 337
Approximations to the modified profile likelihoodp. 340
Discussion and referencesp. 352
Exercisesp. 352
Data sets used in the examplesp. 354
Referencesp. 362
Author indexp. 374
Subject indexp. 377
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780198506508
ISBN-10: 0198506503
Series: Oxford Statistical Science Series
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 392
Published: 1st December 2000
Publisher: Oxford University Press
Country of Publication: GB
Dimensions (cm): 23.67 x 16.05  x 2.74
Weight (kg): 0.52

Earn 432 Qantas Points
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