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Inference and Asymptotics (Chapman & Hall/CRC Monographs on Statistics and Applied Probability) - Hardcover
Synopsis
This book provides a systematic account of some developments in asymptotic parametric inference from a likelihood-based perspective. It focuses on first-order asymptotic theory, and discusses the need for higher-order theory.
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About the Author
D.R. Cox
From the Back Cover
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.
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Inference and asymptotics O.E. Barndorff-Nielsen and D.R. Cox. Monographs on statistics and applied probability 52.
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Inference and Asymptotics
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Chapman And Hall Springer Netherlands, Routledge CRC, 1994
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ISBN 13: 9780412494406
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Inference and Asymptotics (Monographs on Statistics and Applied Probability)
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