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.

Download or read book The Asymptotic Distribution of Eigenvalues of Partial Differential Operators written by Yu Safarov and published by American Mathematical Soc.. This book was released on 1997 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work studies the eigenvalues of elliptic linear boundary value problems. Its main content is a set of asymptotic formulas describing the distribution of eigenvalues with high sequential numbers, providing a basic introduction to mathematical concepts and tools.

Download or read book Asymptotic Distribution Theory in Nonparametric Statistics written by Manfred Denker and published by Springer-Verlag. This book was released on 2013-07-02 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book On the Asymptotic Distribution of the Likelihood Ratio in Some Problems on Mixed Variate Populations written by Junjirō Ogawa and published by . This book was released on 1957 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Asymptotic Theory of Statistics and Probability written by Anirban DasGupta and published by Springer Science & Business Media. This book was released on 2008-03-07 with total page 726 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Asymptotic Statistics written by Manfred Denker and published by Birkhäuser. This book was released on 2012-12-06 with total page 121 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 {sect}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)

Download or read book The Asymptotic Distribution of an Estimate of a Location Parameter for Truncated Samples written by Rajiv Lochan Gupta and published by . This book was released on 1969 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Statistical Estimation written by I.A. Ibragimov and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: when certain parameters in the problem tend to limiting values (for example, when the sample size increases indefinitely, the intensity of the noise ap proaches zero, etc.) To address the problem of asymptotically optimal estimators consider the following important case. Let X 1, X 2, ... , X n be independent observations with the joint probability density !(x,O) (with respect to the Lebesgue measure on the real line) which depends on the unknown patameter o e 9 c R1. It is required to derive the best (asymptotically) estimator 0:( X b ... , X n) of the parameter O. The first question which arises in connection with this problem is how to compare different estimators or, equivalently, how to assess their quality, in terms of the mean square deviation from the parameter or perhaps in some other way. The presently accepted approach to this problem, resulting from A. Wald's contributions, is as follows: introduce a nonnegative function w(0l> ( ), Ob Oe 9 (the loss function) and given two estimators Of and O! n 2 2 the estimator for which the expected loss (risk) Eown(Oj, 0), j = 1 or 2, is smallest is called the better with respect to Wn at point 0 (here EoO is the expectation evaluated under the assumption that the true value of the parameter is 0). Obviously, such a method of comparison is not without its defects.

Download or read book Elements of Large Sample Theory written by E.L. Lehmann and published by Springer Science & Business Media. This book was released on 2004-08-27 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by one of the main figures in twentieth century statistics, this book provides a unified treatment of first-order large-sample theory. It discusses a broad range of applications including introductions to density estimation, the bootstrap, and the asymptotics of survey methodology. The book is written at an elementary level making it accessible to most readers.

Download or read book Elements of Modern Asymptotic Theory with Statistical Applications written by Brendan McCabe and published by Manchester University Press. This book was released on 1993 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Structural Equations with Latent Variables written by Kenneth A. Bollen and published by John Wiley & Sons. This book was released on 2014-08-28 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analysis of Ordinal Categorical Data Alan Agresti Statistical Science Now has its first coordinated manual of methods for analyzing ordered categorical data. This book discusses specialized models that, unlike standard methods underlying nominal categorical data, efficiently use the information on ordering. It begins with an introduction to basic descriptive and inferential methods for categorical data, and then gives thorough coverage of the most current developments, such as loglinear and logit models for ordinal data. Special emphasis is placed on interpretation and application of methods and contains an integrated comparison of the available strategies for analyzing ordinal data. This is a case study work with illuminating examples taken from across the wide spectrum of ordinal categorical applications. 1984 (0 471-89055-3) 287 pp. Regression Diagnostics Identifying Influential Data and Sources of Collinearity David A. Belsley, Edwin Kuh and Roy E. Welsch This book provides the practicing statistician and econometrician with new tools for assessing the quality and reliability of regression estimates. Diagnostic techniques are developed that aid in the systematic location of data points that are either unusual or inordinately influential; measure the presence and intensity of collinear relations among the regression data and help to identify the variables involved in each; and pinpoint the estimated coefficients that are potentially most adversely affected. The primary emphasis of these contributions is on diagnostics, but suggestions for remedial action are given and illustrated. 1980 (0 471-05856-4) 292 pp. Applied Regression Analysis Second Edition Norman Draper and Harry Smith Featuring a significant expansion of material reflecting recent advances, here is a complete and up-to-date introduction to the fundamentals of regression analysis, focusing on understanding the latest concepts and applications of these methods. The authors thoroughly explore the fitting and checking of both linear and nonlinear regression models, using small or large data sets and pocket or high-speed computing equipment. Features added to this Second Edition include the practical implications of linear regression; the Durbin-Watson test for serial correlation; families of transformations; inverse, ridge, latent root and robust regression; and nonlinear growth models. Includes many new exercises and worked examples. 1981 (0 471-02995-5) 709 pp.

Download or read book Asymptotic Statistical Inference written by Shailaja Deshmukh and published by Springer Nature. This book was released on 2021-07-05 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Asymptotic Efficiency of Statistical Estimators Concepts and Higher Order Asymptotic Efficiency written by Masafumi Akahira and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is a collection of results recently obtained by the authors. Most of these have been published, while others are awaitlng publication. Our investigation has two main purposes. Firstly, we discuss higher order asymptotic efficiency of estimators in regular situa tions. In these situations it is known that the maximum likelihood estimator (MLE) is asymptotically efficient in some (not always specified) sense. However, there exists here a whole class of asymptotically efficient estimators which are thus asymptotically equivalent to the MLE. It is required to make finer distinctions among the estimators, by considering higher order terms in the expansions of their asymptotic distributions. Secondly, we discuss asymptotically efficient estimators in non regular situations. These are situations where the MLE or other estimators are not asymptotically normally distributed, or where l 2 their order of convergence (or consistency) is not n / , as in the regular cases. It is necessary to redefine the concept of asympto tic efficiency, together with the concept of the maximum order of consistency. Under the new definition as asymptotically efficient estimator may not always exist. We have not attempted to tell the whole story in a systematic way. The field of asymptotic theory in statistical estimation is relatively uncultivated. So, we have tried to focus attention on such aspects of our recent results which throw light on the area.

Download or read book Statistical Tests Of Nonparametric Hypotheses Asymptotic Theory written by Odile Pons and published by World Scientific. This book was released on 2013-10-04 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: An overview of the asymptotic theory of optimal nonparametric tests is presented in this book. It covers a wide range of topics: Neyman-Pearson and LeCam's theories of optimal tests, the theories of empirical processes and kernel estimators with extensions of their applications to the asymptotic behavior of tests for distribution functions, densities and curves of the nonparametric models defining the distributions of point processes and diffusions. With many new test statistics developed for smooth curves, the reliance on kernel estimators with bias corrections and the weak convergence of the estimators are useful to prove the asymptotic properties of the tests, extending the coverage to semiparametric models. They include tests built from continuously observed processes and observations with cumulative intervals.

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.

Download or read book Asymptotic Laws and Methods in Stochastics written by Donald Dawson and published by Springer. This book was released on 2015-11-12 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains articles arising from a conference in honour of mathematician-statistician Miklόs Csörgő on the occasion of his 80th birthday, held in Ottawa in July 2012. It comprises research papers and overview articles, which provide a substantial glimpse of the history and state-of-the-art of the field of asymptotic methods in probability and statistics, written by leading experts. The volume consists of twenty articles on topics on limit theorems for self-normalized processes, planar processes, the central limit theorem and laws of large numbers, change-point problems, short and long range dependent time series, applied probability and stochastic processes, and the theory and methods of statistics. It also includes Csörgő’s list of publications during more than 50 years, since 1962.

Download or read book Higher Order Asymptotic Theory for Time Series Analysis written by Masanobu Taniguchi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.