Author: Stephen ThursbyPublisher:
ISBN:
Category :
Languages : en
Pages : 336
Book Description
Higher Order Asymptotic Theory Associated with Conditioning on Components of a Sufficient Statistic
Inference and Asymptotics
Author: D.R. CoxPublisher: CRC Press
ISBN: 9780412494406
Category : Mathematics
Languages : en
Pages : 376
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.
Higher Order Asymptotic Theory for Time Series Analysis
Author: Masanobu TaniguchiPublisher: Springer Science & Business Media
ISBN: 146123154X
Category : Mathematics
Languages : en
Pages : 169
Book Description
The initial basis of this book was a series of my research papers, that I listed in References. I have many people to thank for the book's existence. Regarding higher order asymptotic efficiency I thank Professors Kei Takeuchi and M. Akahira for their many comments. I used their concept of efficiency for time series analysis. During the summer of 1983, I had an opportunity to visit The Australian National University, and could elucidate the third-order asymptotics of some estimators. I express my sincere thanks to Professor E.J. Hannan for his warmest encouragement and kindness. Multivariate time series analysis seems an important topic. In 1986 I visited Center for Mul tivariate Analysis, University of Pittsburgh. I received a lot of impact from multivariate analysis, and applied many multivariate methods to the higher order asymptotic theory of vector time series. I am very grateful to the late Professor P.R. Krishnaiah for his cooperation and kindness. In Japan my research was mainly performed in Hiroshima University. There is a research group of statisticians who are interested in the asymptotic expansions in statistics. Throughout this book I often used the asymptotic expansion techniques. I thank all the members of this group, especially Professors Y. Fujikoshi and K. Maekawa foItheir helpful discussion. When I was a student of Osaka University I learned multivariate analysis and time series analysis from Professors Masashi Okamoto and T. Nagai, respectively. It is a pleasure to thank them for giving me much of research background.
Elements of Modern Asymptotic Theory with Statistical Applications
Author: Brendan McCabePublisher: Manchester University Press
ISBN: 9780719030536
Category : Estimation theory
Languages : en
Pages : 338
Book Description
The Asymptotic Theory of Extreme Order Statistics
Author: János GalambosPublisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 440
Book Description
Asymptotic Theory in Probability and Statistics with Applications
Author: T. L. LaiPublisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 560
Book Description
Presents a collection of 18 papers, many of which are surveys, on asymptotic theory in probability and statistics, with applications to a variety of problems. This volume comprises three parts: limit theorems, statistics and applications, and mathematical finance and insurance. It is suitable for graduate students in probability and statistics.
Selected Statistical Papers of Sir David Cox: Volume 2, Foundations of Statistical Inference, Theoretical Statistics, Time Series and Stochastic Processes
Author: David Roxbee CoxPublisher: Cambridge University Press
ISBN: 9780521849401
Category : Business & Economics
Languages : en
Pages : 614
Book Description
Sir David Cox's most important papers, each the subject of a new commentary by Professor Cox.
Index to Theses Accepted for Higher Degrees by the Universities of Great Britain and Ireland and the Council for National Academic Awards
Author: Publisher:
ISBN:
Category : Dissertations, Academic
Languages : en
Pages : 816
Book Description
Inference and Asymptotics
Author: D.R. CoxPublisher: Routledge
ISBN: 1351438565
Category : Mathematics
Languages : en
Pages : 360
Book Description
Our book Asymptotic Techniquesfor Use in Statistics was originally planned as an account of asymptotic statistical theory, but by the time we had completed the mathematical preliminaries it seemed best to publish these separately. The present book, although largely self-contained, takes up the original theme and gives a systematic account of some recent developments in asymptotic parametric inference from a likelihood-based perspective. Chapters 1-4 are relatively elementary and provide first a review of key concepts such as likelihood, sufficiency, conditionality, ancillarity, exponential families and transformation models. Then first-order asymptotic theory is set out, followed by a discussion of the need for higher-order theory. This is then developed in some generality in Chapters 5-8. A final chapter deals briefly with some more specialized issues. The discussion emphasizes concepts and techniques rather than precise mathematical verifications with full attention to regularity conditions and, especially in the less technical chapters, draws quite heavily on illustrative examples. Each chapter ends with outline further results and exercises and with bibliographic notes. Many parts of the field discussed in this book are undergoing rapid further development, and in those parts the book therefore in some respects has more the flavour of a progress report than an exposition of a largely completed theory.
Author: Janos Galambos