Inference And Asymptotics
DOWNLOAD
Download Inference And Asymptotics PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Inference And Asymptotics book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Inference And Asymptotics
DOWNLOAD
Author : D.R. Cox
language : en
Publisher: CRC Press
Release Date : 1994-03-01
Inference And Asymptotics written by D.R. Cox and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-03-01 with Mathematics categories.
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.
Inference And Asymptotics
DOWNLOAD
Author : D.R. Cox
language : en
Publisher: Routledge
Release Date : 2017-10-19
Inference And Asymptotics written by D.R. Cox and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-19 with Mathematics categories.
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.
Asymptotic Theory Of Quantum Statistical Inference Selected Papers
DOWNLOAD
Author : Masahito Hayashi
language : en
Publisher: World Scientific
Release Date : 2005-02-21
Asymptotic Theory Of Quantum Statistical Inference Selected Papers written by Masahito Hayashi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-02-21 with Science categories.
Quantum statistical inference, a research field with deep roots in the foundations of both quantum physics and mathematical statistics, has made remarkable progress since 1990. In particular, its asymptotic theory has been developed during this period. However, there has hitherto been no book covering this remarkable progress after 1990; the famous textbooks by Holevo and Helstrom deal only with research results in the earlier stage (1960s-1970s).This book presents the important and recent results of quantum statistical inference. It focuses on the asymptotic theory, which is one of the central issues of mathematical statistics and had not been investigated in quantum statistical inference until the early 1980s. It contains outstanding papers after Holevo's textbook, some of which are of great importance but are not available now.The reader is expected to have only elementary mathematical knowledge, and therefore much of the content will be accessible to graduate students as well as research workers in related fields. Introductions to quantum statistical inference have been specially written for the book. Asymptotic Theory of Quantum Statistical Inference: Selected Papers will give the reader a new insight into physics and statistical inference.
Asymptotic Optimal Inference For Non Ergodic Models
DOWNLOAD
Author : I. V. Basawa
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Asymptotic Optimal Inference For Non Ergodic Models written by I. V. Basawa and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This monograph contains a comprehensive account of the recent work of the authors and other workers on large sample optimal inference for non-ergodic models. The non-ergodic family of models can be viewed as an extension of the usual Fisher-Rao model for asymptotics, referred to here as an ergodic family. The main feature of a non-ergodic model is that the sample Fisher information, appropriately normed, converges to a non-degenerate random variable rather than to a constant. Mixture experiments, growth models such as birth processes, branching processes, etc. , and non-stationary diffusion processes are typical examples of non-ergodic models for which the usual asymptotics and the efficiency criteria of the Fisher-Rao-Wald type are not directly applicable. The new model necessitates a thorough review of both technical and qualitative aspects of the asymptotic theory. The general model studied includes both ergodic and non-ergodic families even though we emphasise applications of the latter type. The plan to write the monograph originally evolved through a series of lectures given by the first author in a graduate seminar course at Cornell University during the fall of 1978, and by the second author at the University of Munich during the fall of 1979. Further work during 1979-1981 on the topic has resolved many of the outstanding conceptual and technical difficulties encountered previously. While there are still some gaps remaining, it appears that the mainstream development in the area has now taken a more definite shape.
Asymptotics In Statistics
DOWNLOAD
Author : Lucien Le Cam
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Asymptotics In Statistics written by Lucien Le Cam and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
In the summer of 1968 one of the present authors (LLC) had the pleasure of giving a sequence of lectures at the University of Mon treal. Lecture notes were collected and written out by Drs. Catherine Doleans, Jean Haezendonck and Roch Roy. They were published in French by the Presses of the University of Montreal as part of their series of Seminaires de Mathematiques Superieures. Twenty years later it was decided that a Chinese translation could be useful, but upon prodding by Professor Shanti Gupta at Purdue we concluded that the notes should be updated and rewritten in English and in Chinese. The present volume is the result of that effort. We have preserved the general outline of the lecture notes, but we have deleted obsolete material and sketched some of the results acquired during the past twenty years. This means that while the original notes concentrated on the LAN situation we have included here some results of Jeganathan and others on the LAMN case. Also included are versions of the Hajek-Le Cam asymptotic minimax and convolution theorems with some of their implications. We have not attempted to give complete coverage of the subject and have often stated theorems without indicating their proofs.
Inference And Asymptotics
DOWNLOAD
Author : Ole E. Barndorff-Nielsen
language : en
Publisher:
Release Date : 2001
Inference And Asymptotics written by Ole E. Barndorff-Nielsen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with MATHEMATICS categories.
Asymptotic Statistical Inference
DOWNLOAD
Author : Shailaja Deshmukh
language : en
Publisher: Springer Nature
Release Date : 2021-07-05
Asymptotic Statistical Inference written by Shailaja Deshmukh and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-05 with Mathematics categories.
The book presents the fundamental concepts from asymptotic statistical inference theory, elaborating on some basic large sample optimality properties of estimators and some test procedures. The most desirable property of consistency of an estimator and its large sample distribution, with suitable normalization, are discussed, the focus being on the consistent and asymptotically normal (CAN) estimators. It is shown that for the probability models belonging to an exponential family and a Cramer family, the maximum likelihood estimators of the indexing parameters are CAN. The book describes some large sample test procedures, in particular, the most frequently used likelihood ratio test procedure. Various applications of the likelihood ratio test procedure are addressed, when the underlying probability model is a multinomial distribution. These include tests for the goodness of fit and tests for contingency tables. The book also discusses a score test and Wald’s test, their relationship with the likelihood ratio test and Karl Pearson’s chi-square test. An important finding is that, while testing any hypothesis about the parameters of a multinomial distribution, a score test statistic and Karl Pearson’s chi-square test statistic are identical. Numerous illustrative examples of differing difficulty level are incorporated to clarify the concepts. For better assimilation of the notions, various exercises are included in each chapter. Solutions to almost all the exercises are given in the last chapter, to motivate students towards solving these exercises and to enable digestion of the underlying concepts. The concepts from asymptotic inference are crucial in modern statistics, but are difficult to grasp in view of their abstract nature. To overcome this difficulty, keeping up with the recent trend of using R software for statistical computations, the book uses it extensively, for illustrating the concepts, verifying the properties of estimators and carrying out various test procedures. The last section of the chapters presents R codes to reveal and visually demonstrate the hidden aspects of different concepts and procedures. Augmenting the theory with R software is a novel and a unique feature of the book. The book is designed primarily to serve as a text book for a one semester introductory course in asymptotic statistical inference, in a post-graduate program, such as Statistics, Bio-statistics or Econometrics. It will also provide sufficient background information for studying inference in stochastic processes. The book will cater to the need of a concise but clear and student-friendly book introducing, conceptually and computationally, basics of asymptotic inference.
Inference Asymptotics And Applications
DOWNLOAD
Author : Nancy Reid
language : en
Publisher: World Scientific
Release Date : 2017-03-10
Inference Asymptotics And Applications written by Nancy Reid and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-10 with Mathematics categories.
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.
Asymptotic Theory Of Statistics And Probability
DOWNLOAD
Author : Anirban DasGupta
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-03-07
Asymptotic Theory Of Statistics And Probability written by Anirban DasGupta and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-03-07 with Mathematics categories.
This unique book delivers an encyclopedic treatment of classic as well as contemporary large sample theory, dealing with both statistical problems and probabilistic issues and tools. The book is unique in its detailed coverage of fundamental topics. It is written in an extremely lucid style, with an emphasis on the conceptual discussion of the importance of a problem and the impact and relevance of the theorems. There is no other book in large sample theory that matches this book in coverage, exercises and examples, bibliography, and lucid conceptual discussion of issues and theorems.
Asymptotic Statistics
DOWNLOAD
Author : A. W. van der Vaart
language : en
Publisher: Cambridge University Press
Release Date : 2000-06-19
Asymptotic Statistics written by A. W. van der Vaart and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-06-19 with Mathematics categories.
This book is an introduction to the field of asymptotic statistics. The treatment is both practical and mathematically rigorous. In addition to most of the standard topics of an asymptotics course, including likelihood inference, M-estimation, the theory of asymptotic efficiency, U-statistics, and rank procedures, the book also presents recent research topics such as semiparametric models, the bootstrap, and empirical processes and their applications. The topics are organized from the central idea of approximation by limit experiments, which gives the book one of its unifying themes. This entails mainly the local approximation of the classical i.i.d. set up with smooth parameters by location experiments involving a single, normally distributed observation. Thus, even the standard subjects of asymptotic statistics are presented in a novel way. Suitable as a graduate or Master's level statistics text, this book will also give researchers an overview of research in asymptotic statistics.