Inference And Asymptotics

Author : D.R. Cox
Publisher : Routledge
Page : 360 pages
File Size : 41,7 Mb
Release : 2017-10-19
Category : Mathematics
ISBN : 9781351438568

Get Book

Inference and Asymptotics by D.R. Cox Pdf

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 : D.R. Cox,O.E. Barndorff-Nielsen
Publisher : CRC Press
Page : 376 pages
File Size : 55,6 Mb
Release : 1994-03-01
Category : Mathematics
ISBN : 041249440X

Get Book

Inference and Asymptotics by D.R. Cox,O.E. Barndorff-Nielsen Pdf

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 : B. L. S. Prakasa Rao
Publisher : Unknown
Page : 458 pages
File Size : 45,6 Mb
Release : 1987-01-16
Category : Mathematics
ISBN : UOM:39015046271048

Get Book

Asymptotic Theory of Statistical Inference by B. L. S. Prakasa Rao Pdf

Probability and stochastic processes; Limit theorems for some statistics; Asymptotic theory of estimation; Linear parametric inference; Martingale approach to inference; Inference in nonlinear regression; Von mises functionals; Empirical characteristic function and its applications.

Author : Nancy Reid,Torben Martinussen
Publisher : World Scientific
Page : 364 pages
File Size : 40,5 Mb
Release : 2017-03-10
Category : Mathematics
ISBN : 9789813207875

Get Book

Inference, Asymptotics, and Applications by Nancy Reid,Torben Martinussen Pdf

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 : I. V. Basawa,D. J. Scott
Publisher : Springer Science & Business Media
Page : 183 pages
File Size : 50,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461255055

Get Book

Asymptotic Optimal Inference for Non-ergodic Models by I. V. Basawa,D. J. Scott Pdf

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.

Author : Jana Jurecková,Pranab Kumar Sen
Publisher : John Wiley & Sons
Page : 496 pages
File Size : 52,8 Mb
Release : 1996-04-19
Category : Mathematics
ISBN : 0471822213

Get Book

Robust Statistical Procedures by Jana Jurecková,Pranab Kumar Sen Pdf

A broad and unified methodology for robust statistics—with exciting new applications Robust statistics is one of the fastest growing fields in contemporary statistics. It is also one of the more diverse and sometimes confounding areas, given the many different assessments and interpretations of robustness by theoretical and applied statisticians. This innovative book unifies the many varied, yet related, concepts of robust statistics under a sound theoretical modulation. It seamlessly integrates asymptotics and interrelations, and provides statisticians with an effective system for dealing with the interrelations between the various classes of procedures. Drawing on the expertise of researchers from around the world, and covering over a decade's worth of developments in the field, Robust Statistical Procedures: Asymptotics and Interrelations: Discusses both theory and applications in its two parts, from the fundamentals to robust statistical inference Thoroughly explores the interrelations between diverse classes of procedures, unlike any other book Compares nonparametric procedures with robust statistics, explaining in detail asymptotic representations for various estimators Provides a timesaving list of mathematical tools for the problems under discussion Keeps mathematical abstractions to a minimum, in spite of its largely theoretical content Includes useful problems and exercises at the end of each chapter Offers strategies for more complex models when using robust statistical procedures Self-contained and rounded in approach, this book is invaluable for both applied statisticians and theoretical researchers; for graduate students in mathematical statistics; and for anyone interested in the influence of this methodology.

Author : Lucien Le Cam,Grace Lo Yang
Publisher : Springer Science & Business Media
Page : 299 pages
File Size : 42,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461211662

Get Book

Asymptotics in Statistics by Lucien Le Cam,Grace Lo Yang Pdf

This is the second edition of a coherent introduction to the subject of asymptotic statistics as it has developed over the past 50 years. It differs from the first edition in that it is now more 'reader friendly' and also includes a new chapter on Gaussian and Poisson experiments, reflecting their growing role in the field. Most of the subsequent chapters have been entirely rewritten and the nonparametrics of Chapter 7 have been amplified. The volume is not intended to replace monographs on specialized subjects, but will help to place them in a coherent perspective. It thus represents a link between traditional material - such as maximum likelihood, and Wald's Theory of Statistical Decision Functions -- together with comparison and distances for experiments. Much of the material has been taught in a second year graduate course at Berkeley for 30 years.

Author : Anirban DasGupta
Publisher : Springer Science & Business Media
Page : 726 pages
File Size : 42,9 Mb
Release : 2008-03-07
Category : Mathematics
ISBN : 9780387759708

Get Book

Asymptotic Theory of Statistics and Probability by Anirban DasGupta Pdf

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.

Author : Ishwar V. Basawa,David John Scott
Publisher : Unknown
Page : 170 pages
File Size : 55,9 Mb
Release : 1983
Category : Asymptotic efficiencies (Statistics)
ISBN : 3540908102

Get Book

Asymptotic Optimal Inference for Non-ergodic Models by Ishwar V. Basawa,David John Scott Pdf

Author : Luigi Pace,Alessandra Salvan
Publisher : World Scientific
Page : 584 pages
File Size : 43,8 Mb
Release : 1997-08-05
Category : Mathematics
ISBN : 9812386947

Get Book

Principles of Statistical Inference by Luigi Pace,Alessandra Salvan Pdf

In this book, an integrated introduction to statistical inference is provided from a frequentist likelihood-based viewpoint. Classical results are presented together with recent developments, largely built upon ideas due to R.A. Fisher. The term ?neo-Fisherian? highlights this.After a unified review of background material (statistical models, likelihood, data and model reduction, first-order asymptotics) and inference in the presence of nuisance parameters (including pseudo-likelihoods), a self-contained introduction is given to exponential families, exponential dispersion models, generalized linear models, and group families. Finally, basic results of higher-order asymptotics are introduced (index notation, asymptotic expansions for statistics and distributions, and major applications to likelihood inference).The emphasis is more on general concepts and methods than on regularity conditions. Many examples are given for specific statistical models. Each chapter is supplemented with problems and bibliographic notes. This volume can serve as a textbook in intermediate-level undergraduate and postgraduate courses in statistical inference.

Author : A. W. van der Vaart
Publisher : Cambridge University Press
Page : 128 pages
File Size : 45,7 Mb
Release : 2000-06-19
Category : Mathematics
ISBN : 9781107268449

Get Book

Asymptotic Statistics by A. W. van der Vaart Pdf

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.

Author : Robert E. Kass,Paul W. Vos
Publisher : John Wiley & Sons
Page : 376 pages
File Size : 55,6 Mb
Release : 2011-09-09
Category : Mathematics
ISBN : 9781118165973

Get Book

Geometrical Foundations of Asymptotic Inference by Robert E. Kass,Paul W. Vos Pdf

Differential geometry provides an aesthetically appealing and oftenrevealing view of statistical inference. Beginning with anelementary treatment of one-parameter statistical models and endingwith an overview of recent developments, this is the first book toprovide an introduction to the subject that is largely accessibleto readers not already familiar with differential geometry. It alsogives a streamlined entry into the field to readers with richermathematical backgrounds. Much space is devoted to curvedexponential families, which are of interest not only because theymay be studied geometrically but also because they are analyticallyconvenient, so that results may be derived rigorously. In addition,several appendices provide useful mathematical material on basicconcepts in differential geometry. Topics covered include thefollowing: * Basic properties of curved exponential families * Elements of second-order, asymptotic theory * The Fisher-Efron-Amari theory of information loss and recovery * Jeffreys-Rao information-metric Riemannian geometry * Curvature measures of nonlinearity * Geometrically motivated diagnostics for exponential familyregression * Geometrical theory of divergence functions * A classification of and introduction to additional work in thefield

Author : Dennis D. Boos,L A Stefanski
Publisher : Springer Science & Business Media
Page : 567 pages
File Size : 45,7 Mb
Release : 2013-02-06
Category : Mathematics
ISBN : 9781461448181

Get Book

Essential Statistical Inference by Dennis D. Boos,L A Stefanski Pdf

​This book is for students and researchers who have had a first year graduate level mathematical statistics course. It covers classical likelihood, Bayesian, and permutation inference; an introduction to basic asymptotic distribution theory; and modern topics like M-estimation, the jackknife, and the bootstrap. R code is woven throughout the text, and there are a large number of examples and problems. An important goal has been to make the topics accessible to a wide audience, with little overt reliance on measure theory. A typical semester course consists of Chapters 1-6 (likelihood-based estimation and testing, Bayesian inference, basic asymptotic results) plus selections from M-estimation and related testing and resampling methodology. Dennis Boos and Len Stefanski are professors in the Department of Statistics at North Carolina State. Their research has been eclectic, often with a robustness angle, although Stefanski is also known for research concentrated on measurement error, including a co-authored book on non-linear measurement error models. In recent years the authors have jointly worked on variable selection methods. ​

Author : Jiming Jiang
Publisher : CRC Press
Page : 252 pages
File Size : 43,9 Mb
Release : 2017-09-19
Category : Mathematics
ISBN : 9781498700467

Get Book

Asymptotic Analysis of Mixed Effects Models by Jiming Jiang Pdf

Large sample techniques are fundamental to all fields of statistics. Mixed effects models, including linear mixed models, generalized linear mixed models, non-linear mixed effects models, and non-parametric mixed effects models are complex models, yet, these models are extensively used in practice. This monograph provides a comprehensive account of asymptotic analysis of mixed effects models. The monograph is suitable for researchers and graduate students who wish to learn about asymptotic tools and research problems in mixed effects models. It may also be used as a reference book for a graduate-level course on mixed effects models, or asymptotic analysis.

Author : A. R. Brazzale,A. C. Davison,N. Reid
Publisher : Cambridge University Press
Page : 211 pages
File Size : 41,7 Mb
Release : 2007-05-31
Category : Mathematics
ISBN : 9781139463836

Get Book

Applied Asymptotics by A. R. Brazzale,A. C. Davison,N. Reid Pdf

In fields such as biology, medical sciences, sociology, and economics researchers often face the situation where the number of available observations, or the amount of available information, is sufficiently small that approximations based on the normal distribution may be unreliable. Theoretical work over the last quarter-century has led to new likelihood-based methods that lead to very accurate approximations in finite samples, but this work has had limited impact on statistical practice. This book illustrates by means of realistic examples and case studies how to use the new theory, and investigates how and when it makes a difference to the resulting inference. The treatment is oriented towards practice and comes with code in the R language (available from the web) which enables the methods to be applied in a range of situations of interest to practitioners. The analysis includes some comparisons of higher order likelihood inference with bootstrap or Bayesian methods.