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Author | : D.R. Cox |
Publisher | : Routledge |
Total Pages | : 360 |
Release | : 2017-10-19 |
Genre | : Mathematics |
ISBN | : 1351438565 |
Download Inference and Asymptotics Book in PDF, ePub and Kindle
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 | : Anirban DasGupta |
Publisher | : Springer Science & Business Media |
Total Pages | : 727 |
Release | : 2008-02-06 |
Genre | : Mathematics |
ISBN | : 0387759719 |
Download Asymptotic Theory of Statistics and Probability Book in PDF, ePub and Kindle
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 | : O. E. Barndorff-Nielsen |
Publisher | : Springer |
Total Pages | : 360 |
Release | : 2013-08-23 |
Genre | : Mathematics |
ISBN | : 9781489932112 |
Download Inference and Asymptotics Book in PDF, ePub and Kindle
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 | : Luigi Pace |
Publisher | : World Scientific Publishing Company |
Total Pages | : 557 |
Release | : 1997-08-05 |
Genre | : Mathematics |
ISBN | : 9813103019 |
Download Principles Of Statistical Inference From A Neo-fisherian Perspective Book in PDF, ePub and Kindle
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 | : Nancy Reid |
Publisher | : World Scientific |
Total Pages | : 364 |
Release | : 2017-03-10 |
Genre | : Mathematics |
ISBN | : 9813207876 |
Download Inference, Asymptotics, and Applications Book in PDF, ePub and Kindle
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 | : Masanobu Taniguchi |
Publisher | : Springer Science & Business Media |
Total Pages | : 671 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 146121162X |
Download Asymptotic Theory of Statistical Inference for Time Series Book in PDF, ePub and Kindle
The primary aim of this book is to provide modern statistical techniques and theory for stochastic processes. The stochastic processes mentioned here are not restricted to the usual AR, MA, and ARMA processes. A wide variety of stochastic processes, including non-Gaussian linear processes, long-memory processes, nonlinear processes, non-ergodic processes and diffusion processes are described. The authors discuss estimation and testing theory and many other relevant statistical methods and techniques.
Author | : A. R. Brazzale |
Publisher | : Cambridge University Press |
Total Pages | : 256 |
Release | : 2007-05-31 |
Genre | : Business & Economics |
ISBN | : 9780521847032 |
Download Applied Asymptotics Book in PDF, ePub and Kindle
First practical treatment of small-sample asymptotics, enabling practitioners to apply new methods with confidence.
Author | : I. V. Basawa |
Publisher | : Springer Science & Business Media |
Total Pages | : 183 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461255058 |
Download Asymptotic Optimal Inference for Non-ergodic Models Book in PDF, ePub and Kindle
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 | : Lucien Le Cam |
Publisher | : Springer Science & Business Media |
Total Pages | : 299 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461211662 |
Download Asymptotics in Statistics Book in PDF, ePub and Kindle
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 | : Subir Ghosh |
Publisher | : CRC Press |
Total Pages | : 858 |
Release | : 1999-02-18 |
Genre | : Mathematics |
ISBN | : 1482269775 |
Download Asymptotics, Nonparametrics, and Time Series Book in PDF, ePub and Kindle
"Contains over 2500 equations and exhaustively covers not only nonparametrics but also parametric, semiparametric, frequentist, Bayesian, bootstrap, adaptive, univariate, and multivariate statistical methods, as well as practical uses of Markov chain models."