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Asymptotic Expansions For General Statistical Models
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Book Synopsis Asymptotic Expansions for General Statistical Models by : Johann Pfanzagl
Download or read book Asymptotic Expansions for General Statistical Models written by Johann Pfanzagl and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: 0.1. The aim of the book Our "Contributions to a General Asymptotic Statistical Theory" (Springer Lecture Notes in Statistics, Vol. 13, 1982, called "Vol. I" in the following) suggest to describe the local structure of a general family ~ of probability measures by its tangent space, and the local behavior of a functional K: ~ ~~k by its gradient. Starting from these basic concepts, asymptotic envelope power functions for tests and asymptotic bounds for the concentration of estimators are obtained, and heuristic procedures are suggested for the construction of test- and estimator-sequences attaining these bounds. In the present volume, these asymptotic investigations are carried one step further: From approximations by limit distributions to approximations by Edgeworth expansions, 1 2 adding one term (of order n- / ) to the limit distribution. As in Vol. I, the investigation is "general" in the sense of dealing with arbitrary families of probability measures and arbitrary functionals. The investigation is special in the sense that it is restricted to statistical procedures based on independent, identically distributed observations. 2 Moreover, it is special in the sense that its concern are "regular" models (i.e. families of probability measures and functionals which are subject to certain general conditions, like differentiability). Irregular models are certainly of mathematical interest. Since they are hardly of any practical relevance, it appears justifiable to exclude them at this stage of the investigation.
Book Synopsis Asymptotic Techniques for Use in Statistics by : O. E. Barndorff-Nielsen
Download or read book Asymptotic Techniques for Use in Statistics written by O. E. Barndorff-Nielsen and published by Springer. This book was released on 2013-08-23 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use in statistical theory of approximate arguments based on such methods as local linearization (the delta method) and approxi mate normality has a long history. Such ideas play at least three roles. First they may give simple approximate answers to distributional problems where an exact solution is known in principle but difficult to implement. The second role is to yield higher-order expansions from which the accuracy of simple approximations may be assessed and where necessary improved. Thirdly the systematic development of a theoretical approach to statistical inference that will apply to quite general families of statistical models demands an asymptotic formulation, as far as possible one that will recover 'exact' results where these are available. The approximate arguments are developed by supposing that some defining quantity, often a sample size but more generally an amount of information, becomes large: it must be stressed that this is a technical device for generating approximations whose adequacy always needs assessing, rather than a 'physical' limiting notion. Of the three roles outlined above, the first two are quite close to the traditional roles of asymptotic expansions in applied mathematics and much ofthe very extensive literature on the asymptotic expansion of integrals and of the special functions of mathematical physics is quite directly relevant, although the recasting of these methods into a probability mould is quite often enlightening.
Book Synopsis Asymptotic Statistics by : Manfred Denker
Download or read book Asymptotic Statistics written by Manfred Denker and published by Springer Science & Business Media. This book was released on 1990-04-01 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes are based on lectures presented during the seminar on " Asymptotic Statistics" held at SchloB Reisensburg, Gunzburg, May 29-June 5, 1988. They consist of two parts, the theory of asymptotic expansions in statistics and probabilistic aspects of the asymptotic distribution theory in nonparametric statistics. Our intention is to provide a comprehensive presentation of these two subjects, leading from elementary facts to the advanced theory and recent results. Prospects for further research are also included. We would like to thank all participants for their stimulating discussions and their interest in the subjects, which made lecturing very pleasant. Special thanks are due H. Zimmer for her excellent typing. We would also like to take this opportunity to to express our thanks to the Gesellschaft fur mathematische Forschung and to the Deutsche Mathematiker Vereinigung, especially to Professor G. Fischer, for the opportunity to present these lectures and to the Birkhauser Verlag for the publication of these lecture notes. R. Bhattacharya, M. Denker Part I: Asymptotic Expansions in Statistics Rabi Bhattacharya 11 §1. CRAMER-EDGEWORTH EXPANSIONS Let Q be a probability measure on (IRk, B"), B" denoting the Borel sigmafield on IR". Assume that the s - th absolute moment of Q is finite, (1.1) P. := J II x lis Q(dx)
Book Synopsis Expansions and Asymptotics for Statistics by : Christopher G. Small
Download or read book Expansions and Asymptotics for Statistics written by Christopher G. Small and published by CRC Press. This book was released on 2010-05-07 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotic methods provide important tools for approximating and analysing functions that arise in probability and statistics. Moreover, the conclusions of asymptotic analysis often supplement the conclusions obtained by numerical methods. Providing a broad toolkit of analytical methods, Expansions and Asymptotics for Statistics shows how asymptoti
Book Synopsis Developments in Statistics by : Paruchuri R. Krishnaiah
Download or read book Developments in Statistics written by Paruchuri R. Krishnaiah and published by Academic Press. This book was released on 2014-06-28 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: Development in Statistics, Volume 3 is a collection of papers that deals with asymptotic expansions in parametric statistical theory, orthogonal models for contingency tables, statistical concepts in economic analysis, and an exposition of path analysis. One paper presents an inference model based on a sample of independent identically distributed observations to arrive at a general statistical theory founded on asymptotic methods. Another paper discusses the applicability of statistical concepts to economics and related areas, with emphasis on not-so-obvious applications (known as utility and expected loss). The paper explains information theory concepts for the measurement of income inequality, intergenerational occupational mobility, as well as to first- and second-order moments of univariate and bivariate distributions (such as measurements applied to the cost of living and of real income). One paper notes that the starting point in path analysis is a linear predictor (in the least-squares sense) for one random variable in terms of a number of others. The paper adds that the work of Koopmans and Hood (1953) on econometrics is part of the starting point. Statisticians, economists, mathematicians, students, and professors of calculus or advanced mathematics will surely appreciate the collection.
Book Synopsis Normal Approximation and Asymptotic Expansions by : Rabi N. Bhattacharya
Download or read book Normal Approximation and Asymptotic Expansions written by Rabi N. Bhattacharya and published by SIAM. This book was released on 2010-11-11 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: -Fourier analysis, --
Book Synopsis Analytic Statistical Models by : Ib M. Skovgaard
Download or read book Analytic Statistical Models written by Ib M. Skovgaard and published by IMS. This book was released on 1990 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asymptotic Techniques for Use in Statistics by : O. E. Barndorff-Nielsen
Download or read book Asymptotic Techniques for Use in Statistics written by O. E. Barndorff-Nielsen and published by Springer. This book was released on 1989-03 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use in statistical theory of approximate arguments based on such methods as local linearization (the delta method) and approxi mate normality has a long history. Such ideas play at least three roles. First they may give simple approximate answers to distributional problems where an exact solution is known in principle but difficult to implement. The second role is to yield higher-order expansions from which the accuracy of simple approximations may be assessed and where necessary improved. Thirdly the systematic development of a theoretical approach to statistical inference that will apply to quite general families of statistical models demands an asymptotic formulation, as far as possible one that will recover 'exact' results where these are available. The approximate arguments are developed by supposing that some defining quantity, often a sample size but more generally an amount of information, becomes large: it must be stressed that this is a technical device for generating approximations whose adequacy always needs assessing, rather than a 'physical' limiting notion. Of the three roles outlined above, the first two are quite close to the traditional roles of asymptotic expansions in applied mathematics and much ofthe very extensive literature on the asymptotic expansion of integrals and of the special functions of mathematical physics is quite directly relevant, although the recasting of these methods into a probability mould is quite often enlightening.
Book Synopsis Principles Of Statistical Inference From A Neo-fisherian Perspective by : Luigi Pace
Download or read book Principles Of Statistical Inference From A Neo-fisherian Perspective written by Luigi Pace and published by World Scientific Publishing Company. This book was released on 1997-08-05 with total page 557 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Asymptotic Statistics by : A. W. van der Vaart
Download or read book Asymptotic Statistics written by A. W. van der Vaart and published by Cambridge University Press. This book was released on 2000-06-19 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 the latest research in asymptotic statistics.
Book Synopsis Normal Approximation and Asymptotic Expansions by : Rabindra Nath Bhattacharya
Download or read book Normal Approximation and Asymptotic Expansions written by Rabindra Nath Bhattacharya and published by . This book was released on 1986 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although this was first published in 1976, it has gained new significance and renewed interest among statisticians due to the developments of modern statistical techniques such as the bootstrap, the efficacy of which can be ascertained by asymptotic expansions. This also is the only book containing a detailed treatment of various refinements of the multivariate central limit theorem (CLT), including Berry-Essen-type error bounds for probabilities of general classes of functions and sets, and asymptotic expansions for both lattice and non-lattice distributions.
Book Synopsis A Course in Mathematical Statistics and Large Sample Theory by : Rabi Bhattacharya
Download or read book A Course in Mathematical Statistics and Large Sample Theory written by Rabi Bhattacharya and published by Springer. This book was released on 2016-08-13 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level textbook is primarily aimed at graduate students of statistics, mathematics, science, and engineering who have had an undergraduate course in statistics, an upper division course in analysis, and some acquaintance with measure theoretic probability. It provides a rigorous presentation of the core of mathematical statistics. Part I of this book constitutes a one-semester course on basic parametric mathematical statistics. Part II deals with the large sample theory of statistics - parametric and nonparametric, and its contents may be covered in one semester as well. Part III provides brief accounts of a number of topics of current interest for practitioners and other disciplines whose work involves statistical methods.
Book Synopsis Asymptotic Statistics by : A. W. van der Vaart
Download or read book Asymptotic Statistics written by A. W. van der Vaart and published by Cambridge University Press. This book was released on 2000-06-19 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Asymptotic Approximations of Integrals by : R. Wong
Download or read book Asymptotic Approximations of Integrals written by R. Wong and published by SIAM. This book was released on 2001-01-01 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotic methods are frequently used in many branches of both pure and applied mathematics, and this classic text remains the most up-to-date book dealing with one important aspect of this area, namely, asymptotic approximations of integrals. In Asymptotic Approximations of Integrals, all results are proved rigorously, and many of the approximation formulas are accompanied by error bounds. A thorough discussion on multidimensional integrals is given, and references are provided. The book contains the "distributional method," which is not available elsewhere. Most of the examples in this text come from concrete applications. Since its publication twelve years ago, significant developments have occurred in the general theory of asymptotic expansions, including smoothing of the Stokes phenomenon, uniform exponentially improved asymptotic expansions, and hyperasymptotics. These new concepts belong to the area now known as "exponential asymptotics." Expositions of these new theories are available in papers published in various journals, but not yet in book form. Audience: this book can be used either as a text for graduate students in mathematics, physics, and engineering or as a reference for research workers in these fields.
Book Synopsis Asymptotic Theory of Testing Statistical Hypotheses by : Vladimir E. Bening
Download or read book Asymptotic Theory of Testing Statistical Hypotheses written by Vladimir E. Bening and published by Walter de Gruyter. This book was released on 2011-08-30 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is devoted to the publication of high-level monographs and surveys which cover the whole spectrum of probability and statistics. The books of the series are addressed to both experts and advanced students.
Book Synopsis Inference and Asymptotics by : D.R. Cox
Download or read book Inference and Asymptotics written by D.R. Cox and published by Routledge. This book was released on 2017-10-19 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Encyclopedia of Statistical Sciences, Volume 1 by :
Download or read book Encyclopedia of Statistical Sciences, Volume 1 written by and published by John Wiley & Sons. This book was released on 2005-12-16 with total page 722 pages. Available in PDF, EPUB and Kindle. Book excerpt: ENCYCLOPEDIA OF STATISTICAL SCIENCES
