Download or read book von Mises Calculus For Statistical Functionals written by L. T. Fernholz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: About forty years ago, Richard von Mises proposed a theory for the analysis of the asymptotic behavior of nonlinear statistical functionals based on the differentiability properties of these functionals. His theory was largely neglected until the late 1960's when it experienced a renaissance due to developments in the field of robust statistics. In particular, the "Volterra" derivative used by von Mises evolved into the influence curve, which was used to provide information about the sensi ti vity of an estimator to outliers, as well as the estimator's asymptot ic variance. Moreover, with the "Princeton Robustness Study" (Andrews et al. (1972)), there began a proliferation of new robust statistics, and the formal von Mises calculations provided a convenient heuristic tool for the analysis of the asymptotic distributions of these statistics. In the last few years, these calculations have been put in a more rigorous setting based on the Frechet and Hadamard, or compact, derivatives. The purpose of these notes is to provide von Mises' theory with a rig orous mathematical framework which is sufficiently straightforward so that it can be applied routinely with little more effort than is required for the calculation of the influence curve. The approach presented here is based on the Hadamard derivative and is applicable to diverse forms of sta tistical functionals.

Download or read book Encyclopedia of Statistical Sciences Volume 12 written by and published by John Wiley & Sons. This book was released on 2005-12-16 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: ENCYCLOPEDIA OF STATISTICAL SCIENCES

Download or read book von Mises Calculus For Statistical Functionals written by L. T. Fernholz and published by Springer. This book was released on 1983-08-29 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: About forty years ago, Richard von Mises proposed a theory for the analysis of the asymptotic behavior of nonlinear statistical functionals based on the differentiability properties of these functionals. His theory was largely neglected until the late 1960's when it experienced a renaissance due to developments in the field of robust statistics. In particular, the "Volterra" derivative used by von Mises evolved into the influence curve, which was used to provide information about the sensi­ ti vity of an estimator to outliers, as well as the estimator's asymptot­ ic variance. Moreover, with the "Princeton Robustness Study" (Andrews et al. (1972)), there began a proliferation of new robust statistics, and the formal von Mises calculations provided a convenient heuristic tool for the analysis of the asymptotic distributions of these statistics. In the last few years, these calculations have been put in a more rigorous setting based on the Frechet and Hadamard, or compact, derivatives. The purpose of these notes is to provide von Mises' theory with a rig­ orous mathematical framework which is sufficiently straightforward so that it can be applied routinely with little more effort than is required for the calculation of the influence curve. The approach presented here is based on the Hadamard derivative and is applicable to diverse forms of sta­ tistical functionals.

Download or read book Aspects of Statistical Inference written by A. H. Welsh and published by John Wiley & Sons. This book was released on 2011-09-15 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: Relevant, concrete, and thorough--the essential data-based text onstatistical inference The ability to formulate abstract concepts and draw conclusionsfrom data is fundamental to mastering statistics. Aspects ofStatistical Inference equips advanced undergraduate and graduatestudents with a comprehensive grounding in statistical inference,including nonstandard topics such as robustness, randomization, andfinite population inference. A. H. Welsh goes beyond the standard texts and expertly synthesizesbroad, critical theory with concrete data and relevant topics. Thetext follows a historical framework, uses real-data sets andstatistical graphics, and treats multiparameter problems, yet isultimately about the concepts themselves. Written with clarity and depth, Aspects of Statistical Inference: * Provides a theoretical and historical grounding in statisticalinference that considers Bayesian, fiducial, likelihood, andfrequentist approaches * Illustrates methods with real-data sets on diabetic retinopathy,the pharmacological effects of caffeine, stellar velocity, andindustrial experiments * Considers multiparameter problems * Develops large sample approximations and shows how to use them * Presents the philosophy and application of robustness theory * Highlights the central role of randomization in statistics * Uses simple proofs to illuminate foundational concepts * Contains an appendix of useful facts concerning expansions,matrices, integrals, and distribution theory Here is the ultimate data-based text for comparing and presentingthe latest approaches to statistical inference.

Download or read book Robust Statistics written by Ricardo A. Maronna and published by John Wiley & Sons. This book was released on 2019-01-04 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new edition of this popular text on robust statistics, thoroughly updated to include new and improved methods and focus on implementation of methodology using the increasingly popular open-source software R. Classical statistics fail to cope well with outliers associated with deviations from standard distributions. Robust statistical methods take into account these deviations when estimating the parameters of parametric models, thus increasing the reliability of fitted models and associated inference. This new, second edition of Robust Statistics: Theory and Methods (with R) presents a broad coverage of the theory of robust statistics that is integrated with computing methods and applications. Updated to include important new research results of the last decade and focus on the use of the popular software package R, it features in-depth coverage of the key methodology, including regression, multivariate analysis, and time series modeling. The book is illustrated throughout by a range of examples and applications that are supported by a companion website featuring data sets and R code that allow the reader to reproduce the examples given in the book. Unlike other books on the market, Robust Statistics: Theory and Methods (with R) offers the most comprehensive, definitive, and up-to-date treatment of the subject. It features chapters on estimating location and scale; measuring robustness; linear regression with fixed and with random predictors; multivariate analysis; generalized linear models; time series; numerical algorithms; and asymptotic theory of M-estimates. Explains both the use and theoretical justification of robust methods Guides readers in selecting and using the most appropriate robust methods for their problems Features computational algorithms for the core methods Robust statistics research results of the last decade included in this 2nd edition include: fast deterministic robust regression, finite-sample robustness, robust regularized regression, robust location and scatter estimation with missing data, robust estimation with independent outliers in variables, and robust mixed linear models. Robust Statistics aims to stimulate the use of robust methods as a powerful tool to increase the reliability and accuracy of statistical modelling and data analysis. It is an ideal resource for researchers, practitioners, and graduate students in statistics, engineering, computer science, and physical and social sciences.

Download or read book Probability Models and Statistical Analyses for Ranking Data written by Michael A. Fligner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: In June of 1990, a conference was held on Probablity Models and Statisti cal Analyses for Ranking Data, under the joint auspices of the American Mathematical Society, the Institute for Mathematical Statistics, and the Society of Industrial and Applied Mathematicians. The conference took place at the University of Massachusetts, Amherst, and was attended by 36 participants, including statisticians, mathematicians, psychologists and sociologists from the United States, Canada, Israel, Italy, and The Nether lands. There were 18 presentations on a wide variety of topics involving ranking data. This volume is a collection of 14 of these presentations, as well as 5 miscellaneous papers that were contributed by conference participants. We would like to thank Carole Kohanski, summer program coordinator for the American Mathematical Society, for her assistance in arranging the conference; M. Steigerwald for preparing the manuscripts for publication; Martin Gilchrist at Springer-Verlag for editorial advice; and Persi Diaconis for contributing the Foreword. Special thanks go to the anonymous referees for their careful readings and constructive comments. Finally, we thank the National Science Foundation for their sponsorship of the AMS-IMS-SIAM Joint Summer Programs. Contents Preface vii Conference Participants xiii Foreword xvii 1 Ranking Models with Item Covariates 1 D. E. Critchlow and M. A. Fligner 1. 1 Introduction. . . . . . . . . . . . . . . 1 1. 2 Basic Ranking Models and Their Parameters 2 1. 3 Ranking Models with Covariates 8 1. 4 Estimation 9 1. 5 Example. 11 1. 6 Discussion. 14 1. 7 Appendix . 15 1. 8 References.

Download or read book Differential Geometrical Methods in Statistics written by Shun-ichi Amari and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "In this Lecture Note volume the author describes his differential-geometric approach to parametrical statistical problems summarizing the results he had published in a series of papers in the last five years. The author provides a geometric framework for a special class of test and estimation procedures for curved exponential families. ... ... The material and ideas presented in this volume are important and it is recommended to everybody interested in the connection between statistics and geometry ..." #Metrika#1 "More than hundred references are given showing the growing interest in differential geometry with respect to statistics. The book can only strongly be recommended to a geodesist since it offers many new insights into statistics on a familiar ground." #Manuscripta Geodaetica#2

Download or read book Seminar on Empirical Processes written by P. Gaenssler and published by Birkhäuser. This book was released on 2013-11-21 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Advances in GLIM and Statistical Modelling written by Ludwig Fahrmeir and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the published Proceedings of the joint meeting of GUM92 and the 7th International Workshop on Statistical Modelling, held in Munich, Germany from 13 to 17 July 1992. The meeting aimed to bring together researchers interested in the development and applications of generalized linear modelling in GUM and those interested in statistical modelling in its widest sense. This joint meeting built upon the success of previous workshops and GUM conferences. Previous GUM conferences were held in London and Lancaster, and a joint GUM Conference/4th Modelling Workshop was held in Trento. (The Proceedings of previous GUM conferences/Statistical Modelling Workshops are available as numbers 14 , 32 and 57 of the Springer Verlag series of Lecture Notes in Statistics). Workshops have been organized in Innsbruck, Perugia, Vienna, Toulouse and Utrecht. (Proceedings of the Toulouse Workshop appear as numbers 3 and 4 of volume 13 of the journal Computational Statistics and Data Analysis). Much statistical modelling is carried out using GUM, as is apparent from many of the papers in these Proceedings. Thus the Programme Committee were also keen on encouraging papers which addressed problems which are not only of practical importance but which are also relevant to GUM or other software development. The Programme Committee requested both theoretical and applied papers. Thus there are papers in a wide range of practical areas, such as ecology, breast cancer remission and diabetes mortality, banking and insurance, quality control, social mobility, organizational behaviour.

Download or read book Statistical Applications of Jordan Algebras written by James D. Malley and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph brings together my work in mathematical statistics as I have viewed it through the lens of Jordan algebras. Three technical domains are to be seen: applications to random quadratic forms (sums of squares), the investigation of algebraic simplifications of maxi mum likelihood estimation of patterned covariance matrices, and a more wide open mathematical exploration of the algebraic arena from which I have drawn the results used in the statistical problems just mentioned. Chapters 1, 2, and 4 present the statistical outcomes I have developed using the algebraic results that appear, for the most part, in Chapter 3. As a less daunting, yet quite efficient, point of entry into this material, one avoiding most of the abstract algebraic issues, the reader may use the first half of Chapter 4. Here I present a streamlined, but still fully rigorous, definition of a Jordan algebra (as it is used in that chapter) and its essential properties. These facts are then immediately applied to simplifying the M:-step of the EM algorithm for multivariate normal covariance matrix estimation, in the presence of linear constraints, and data missing completely at random. The results presented essentially resolve a practical statistical quest begun by Rubin and Szatrowski [1982], and continued, sometimes implicitly, by many others. After this, one could then return to Chapters 1 and 2 to see how I have attempted to generalize the work of Cochran, Rao, Mitra, and others, on important and useful properties of sums of squares.

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

Download or read book Series Approximation Methods in Statistics written by John E. Kolassa and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book was originally compiled for a course I taught at the University of Rochester in the fall of 1991, and is intended to give advanced graduate students in statistics an introduction to Edgeworth and saddlepoint approximations, and related techniques. Many other authors have also written monographs on this subject, and so this work is narrowly focused on two areas not recently discussed in theoretical text books. These areas are, first, a rigorous consideration of Edgeworth and saddlepoint expansion limit theorems, and second, a survey of the more recent developments in the field. In presenting expansion limit theorems I have drawn heavily 011 notation of McCullagh (1987) and on the theorems presented by Feller (1971) on Edgeworth expansions. For saddlepoint notation and results I relied most heavily on the many papers of Daniels, and a review paper by Reid (1988). Throughout this book I have tried to maintain consistent notation and to present theorems in such a way as to make a few theoretical results useful in as many contexts as possible. This was not only in order to present as many results with as few proofs as possible, but more importantly to show the interconnections between the various facets of asymptotic theory. Special attention is paid to regularity conditions. The reasons they are needed and the parts they play in the proofs are both highlighted.

Download or read book Tools for Statistical Inference written by Martin A. Tanner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: The purpose of the book under review is to give a survey of methods for the Bayesian or likelihood-based analysis of data. The author distinguishes between two types of methods: the observed data methods and the data augmentation ones. The observed data methods are applied directly to the likelihood or posterior density of the observed data. The data augmentation methods make use of the special "missing" data structure of the problem. They rely on an augmentation of the data which simplifies the likelihood or posterior density. #Zentralblatt für Mathematik#

Download or read book Nonparametric Regression Analysis of Longitudinal Data written by Hans-Georg Müller and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph reviews some of the work that has been done for longitudi nal data in the rapidly expanding field of nonparametric regression. The aim is to give the reader an impression of the basic mathematical tools that have been applied, and also to provide intuition about the methods and applications. Applications to the analysis of longitudinal studies are emphasized to encourage the non-specialist and applied statistician to try these methods out. To facilitate this, FORTRAN programs are provided which carry out some of the procedures described in the text. The emphasis of most research work so far has been on the theoretical aspects of nonparametric regression. It is my hope that these techniques will gain a firm place in the repertoire of applied statisticians who realize the large potential for convincing applications and the need to use these techniques concurrently with parametric regression. This text evolved during a set of lectures given by the author at the Division of Statistics at the University of California, Davis in Fall 1986 and is based on the author's Habilitationsschrift submitted to the University of Marburg in Spring 1985 as well as on published and unpublished work. Completeness is not attempted, neither in the text nor in the references. The following persons have been particularly generous in sharing research or giving advice: Th. Gasser, P. Ihm, Y. P. Mack, V. Mammi tzsch, G . G. Roussas, U. Stadtmuller, W. Stute and R.

Download or read book Time Series Analysis of Irregularly Observed Data written by E. Parzen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: With the support of the Office of Naval Research Program on Statistics and Probability (Dr. Edward J. Wegman, Director), The Department of Statistics at Texas A&M University hosted a Symposium on Time Series Analysis of Irregularly Observed Data during the period February 10-13, 1983. The symposium aimed to provide a review of the state of the art, define outstanding problems for research by theoreticians, transmit to practitioners recently developed algorithms, and stimulate interaction between statisticians and researchers in subject matter fields. Attendance was limited to actively involved researchers. This volume contains refereed versions of the papers presented at the Symposium. We would like to express our appreciation to the many colleagues and staff members whose cheerful help made the Symposium a successful happening which was enjoyed socially and intellectually by all participants. I would like to especially thank Dr. Donald W. Marquardt whose interest led me to undertake to organize this Symposium. This volume is dedicated to the world wide community of researchers who develop and apply methods of statistical analysis of time series. r:;) \J Picture Caption Participants in Symposium on Time Series Analysis of Irregularly Observed Data at Texas A&M University, College Station, Texas, February 10-13, 1983 First Row: Henry L. Gray, D. W. Marquardt, P. M. Robinson, Emanuel Parzen, Julia Abrahams, E. Masry, H. L. Weinert, R. H. Shumway.

Download or read book Linear Statistical Inference written by T. Calinski and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: An International Statistical Conference on Linear Inference was held in Poznan, Poland, on June 4-8, 1984. The conference was organized under the auspices of the Polish Section of the Bernoulli Society, the Committee of Mathematical Sciences and the Mathematical Institute of the ,Polish Academy of Sciences. The purpose of the meeting was to bring together scientists from vari ous countries working in the diverse areas of statistical sciences but showing great interest in the advances of research on linear inference taken in its broad sense. Thus, the conference programme included ses sions on Gauss-Markov models, robustness, variance components~ experi mental design, multiple comparisons, multivariate models, computational aspects and on some special topics. 38 papers were read within the vari ous sessions and 5 were presented as posters. At the end of the confer ence a lively general discussion session was held. The conference gathered more than ninety participants from 16 countries, representing both parts of Europe, North America and Asia. Judging from opinions expressed by many participants, the conference was quite suc cessful, well contributing to the dissemination of knowledge and the stimulation of research in different areas linked with statistical li near inference. If the conference was really a success, it was due to all its participants who in various ways were devoting their time and efforts to make the conference fruitful and enjoyable.

Download or read book Infinitely Divisible Statistical Experiments written by Arnold Janssen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: