Download or read book Shrinkage Estimation for Mean and Covariance Matrices written by Hisayuki Tsukuma and published by Springer Nature. This book was released on 2020-04-16 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a self-contained introduction to shrinkage estimation for matrix-variate normal distribution models. More specifically, it presents recent techniques and results in estimation of mean and covariance matrices with a high-dimensional setting that implies singularity of the sample covariance matrix. Such high-dimensional models can be analyzed by using the same arguments as for low-dimensional models, thus yielding a unified approach to both high- and low-dimensional shrinkage estimations. The unified shrinkage approach not only integrates modern and classical shrinkage estimation, but is also required for further development of the field. Beginning with the notion of decision-theoretic estimation, this book explains matrix theory, group invariance, and other mathematical tools for finding better estimators. It also includes examples of shrinkage estimators for improving standard estimators, such as least squares, maximum likelihood, and minimum risk invariant estimators, and discusses the historical background and related topics in decision-theoretic estimation of parameter matrices. This book is useful for researchers and graduate students in various fields requiring data analysis skills as well as in mathematical statistics.
Download or read book Bayesian Thinking Modeling and Computation written by and published by Elsevier. This book was released on 2005-11-29 with total page 1062 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume describes how to develop Bayesian thinking, modelling and computation both from philosophical, methodological and application point of view. It further describes parametric and nonparametric Bayesian methods for modelling and how to use modern computational methods to summarize inferences using simulation. The book covers wide range of topics including objective and subjective Bayesian inferences with a variety of applications in modelling categorical, survival, spatial, spatiotemporal, Epidemiological, software reliability, small area and micro array data. The book concludes with a chapter on how to teach Bayesian thoughts to nonstatisticians. Critical thinking on causal effects Objective Bayesian philosophy Nonparametric Bayesian methodology Simulation based computing techniques Bioinformatics and Biostatistics
Download or read book Shrinkage Estimation written by Dominique Fourdrinier and published by Springer. This book was released on 2018-11-27 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a coherent framework for understanding shrinkage estimation in statistics. The term refers to modifying a classical estimator by moving it closer to a target which could be known a priori or arise from a model. The goal is to construct estimators with improved statistical properties. The book focuses primarily on point and loss estimation of the mean vector of multivariate normal and spherically symmetric distributions. Chapter 1 reviews the statistical and decision theoretic terminology and results that will be used throughout the book. Chapter 2 is concerned with estimating the mean vector of a multivariate normal distribution under quadratic loss from a frequentist perspective. In Chapter 3 the authors take a Bayesian view of shrinkage estimation in the normal setting. Chapter 4 introduces the general classes of spherically and elliptically symmetric distributions. Point and loss estimation for these broad classes are studied in subsequent chapters. In particular, Chapter 5 extends many of the results from Chapters 2 and 3 to spherically and elliptically symmetric distributions. Chapter 6 considers the general linear model with spherically symmetric error distributions when a residual vector is available. Chapter 7 then considers the problem of estimating a location vector which is constrained to lie in a convex set. Much of the chapter is devoted to one of two types of constraint sets, balls and polyhedral cones. In Chapter 8 the authors focus on loss estimation and data-dependent evidence reports. Appendices cover a number of technical topics including weakly differentiable functions; examples where Stein’s identity doesn’t hold; Stein’s lemma and Stokes’ theorem for smooth boundaries; harmonic, superharmonic and subharmonic functions; and modified Bessel functions.
Download or read book Statistical Inference in Stochastic Processes written by N.U. Prabhu and published by CRC Press. This book was released on 1990-12-18 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering both theory and applications, this collection of eleven contributed papers surveys the role of probabilistic models and statistical techniques in image analysis and processing, develops likelihood methods for inference about parameters that determine the drift and the jump mechanism of a di
Download or read book Unbiased Estimators and their Applications written by V.G. Voinov and published by Springer Science & Business Media. This book was released on 1996-01-31 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a continuation of Unbiased Estimators and Their Applications, Vol. I: Univariate Case. It contains problems of parametric point estimation for multivariate probability distributions emphasizing problems of unbiased estimation. The volume consists of four chapters dealing, respectively, with some basic properties of multivariate continuous and discrete distributions, the general theory of point estimation in multivariate case, techniques for constructing unbiased estimators and applications of unbiased estimation theory in the multivariate case. These chapters contain numerous examples, many applications and are followed by a comprehensive Appendix which classifies and lists, in the form of tables, all known results relating to unbiased estimators of parameter functions for multivariate distributions. Audience: This volume will serve as a handbook on point unbiased estimation for researchers whose work involves statistics. It can also be recommended as a supplementary text for undergraduate and graduate students.
Download or read book Theory of Preliminary Test and Stein Type Estimation with Applications written by A. K. Md. Ehsanes Saleh and published by John Wiley & Sons. This book was released on 2006-04-28 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theory of Preliminary Test and Stein-Type Estimation with Applications provides a com-prehensive account of the theory and methods of estimation in a variety of standard models used in applied statistical inference. It is an in-depth introduction to the estimation theory for graduate students, practitioners, and researchers in various fields, such as statistics, engineering, social sciences, and medical sciences. Coverage of the material is designed as a first step in improving the estimates before applying full Bayesian methodology, while problems at the end of each chapter enlarge the scope of the applications. This book contains clear and detailed coverage of basic terminology related to various topics, including: * Simple linear model; ANOVA; parallelism model; multiple regression model with non-stochastic and stochastic constraints; regression with autocorrelated errors; ridge regression; and multivariate and discrete data models * Normal, non-normal, and nonparametric theory of estimation * Bayes and empirical Bayes methods * R-estimation and U-statistics * Confidence set estimation
Download or read book Fundamentals of Statistical Exponential Families written by Lawrence D. Brown and published by IMS. This book was released on 1986 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Applied Statistical Science III written by Mohammad Ahsanullah and published by . This book was released on 1998 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: CONTENTS: Partially Adaptive Rank and Regression Rank Scores Tests in Linear Models; An Analysis of Nonoparametric Smoothers; Supercritical Branching Random Walk in D-Dimensional Random Environment; Lack of Fit Tests in Regression With Non-Random Design; Asymptotics of the Deepest Line; Multivariate Rank Statistics Processes and Change Point Analysis; Improved Estimation of the Parameters of an Autoagressive Gaussian Process Under Uncertain Restrictions; Testing Normality For Censored Data; Large Sample theory For Estimators of the Moments Based On Synthetic Data Under Randomly Right-Censoring; The Stein Phenomenon in Simultaneous Estimation: A Review; Two Techniques of Integration By Parts and Some Applications; Conditional Confidence Intervals of Regression Coefficients Following Rejection of Preliminary Test; Order Preserving Estimators of Eigenvalues of the Scale Matrix in the Multivariate F Distribution Under Stein's Loss Function; Sequential Estimation of the Man of An Exponential Distribution Via Partial Piece Wise Sampling; Recent Developments on Probability Matching Priors; On the Informative Presentation of Likelihood; Bahadur Risk, Exponential Families and Recursive Estimation; Some Quick Estimators Based on Sample Maxima; Inferences of Power Function Distribution Based on Ordered Random Variables; Estimation of the Location Parameter of A Cauchy Distribution Using A Ranked Set Sample; On A Delayed Service Queuing System With Random Server Capacity and Impatient Customers; Canonical Co-ordinated for Graphical Representation of Multivariate Data; Some Single Use Confidence Regions in Multivariate Calibration Problem; The Likelihood Ratio Test of Non-Nested Linear Regression Models; Exact Power of Classical Tests for Bivariate Linear Hypothesis; Characterisation of the Gamma and the Complex Case Wishart Densities; Jack-knife and Robust Estimation for the Parameters in Pharmocokinetes.
Download or read book Continuous Multivariate Distributions Volume 1 written by Samuel Kotz and published by John Wiley & Sons. This book was released on 2004-04-05 with total page 752 pages. Available in PDF, EPUB and Kindle. Book excerpt: Continuous Multivariate Distributions, Volume 1, Second Edition provides a remarkably comprehensive, self-contained resource for this critical statistical area. It covers all significant advances that have occurred in the field over the past quarter century in the theory, methodology, inferential procedures, computational and simulational aspects, and applications of continuous multivariate distributions. In-depth coverage includes MV systems of distributions, MV normal, MV exponential, MV extreme value, MV beta, MV gamma, MV logistic, MV Liouville, and MV Pareto distributions, as well as MV natural exponential families, which have grown immensely since the 1970s. Each distribution is presented in its own chapter along with descriptions of real-world applications gleaned from the current literature on continuous multivariate distributions and their applications.
Download or read book Statistical Decision Theory and Related Topics written by Shanti S. Gupta and published by Academic Press. This book was released on 2014-05-10 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical Decision Theory and Related Topics II is a compendium of papers presented at an international symposium on Statistical Decision Theory and Related Topics held at Purdue University in May, 1976. The researchers invited to participate, and to author papers for this volume, are among the leaders in the field of Statistical Decision Theory. This collection features works on general decision theory, multiple decision theory, optimal experimental design, and robustness. Mathematicians and statisticians will find the book highly insightful and informative.
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1983 with total page 1368 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Aspects of Multivariate Statistical Theory written by Robb J. Muirhead and published by John Wiley & Sons. This book was released on 2009-09-25 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. ". . . the wealth of material on statistics concerning the multivariate normal distribution is quite exceptional. As such it is a very useful source of information for the general statistician and a must for anyone wanting to penetrate deeper into the multivariate field." -Mededelingen van het Wiskundig Genootschap "This book is a comprehensive and clearly written text on multivariate analysis from a theoretical point of view." -The Statistician Aspects of Multivariate Statistical Theory presents a classical mathematical treatment of the techniques, distributions, and inferences based on multivariate normal distribution. Noncentral distribution theory, decision theoretic estimation of the parameters of a multivariate normal distribution, and the uses of spherical and elliptical distributions in multivariate analysis are introduced. Advances in multivariate analysis are discussed, including decision theory and robustness. The book also includes tables of percentage points of many of the standard likelihood statistics used in multivariate statistical procedures. This definitive resource provides in-depth discussion of the multivariate field and serves admirably as both a textbook and reference.
Download or read book Statistical Decision Theory written by James Berger and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: Decision theory is generally taught in one of two very different ways. When of opti taught by theoretical statisticians, it tends to be presented as a set of mathematical techniques mality principles, together with a collection of various statistical procedures. When useful in establishing the optimality taught by applied decision theorists, it is usually a course in Bayesian analysis, showing how this one decision principle can be applied in various practical situations. The original goal I had in writing this book was to find some middle ground. I wanted a book which discussed the more theoretical ideas and techniques of decision theory, but in a manner that was constantly oriented towards solving statistical problems. In particular, it seemed crucial to include a discussion of when and why the various decision prin ciples should be used, and indeed why decision theory is needed at all. This original goal seemed indicated by my philosophical position at the time, which can best be described as basically neutral. I felt that no one approach to decision theory (or statistics) was clearly superior to the others, and so planned a rather low key and impartial presentation of the competing ideas. In the course of writing the book, however, I turned into a rabid Bayesian. There was no single cause for this conversion; just a gradual realization that things seemed to ultimately make sense only when looked at from the Bayesian viewpoint.
Download or read book Theory of Point Estimation written by Erich L. Lehmann and published by Springer Science & Business Media. This book was released on 2006-05-02 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second, much enlarged edition by Lehmann and Casella of Lehmann's classic text on point estimation maintains the outlook and general style of the first edition. All of the topics are updated, while an entirely new chapter on Bayesian and hierarchical Bayesian approaches is provided, and there is much new material on simultaneous estimation. Each chapter concludes with a Notes section which contains suggestions for further study. This is a companion volume to the second edition of Lehmann's "Testing Statistical Hypotheses".
Download or read book Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability written by Jerzy Neyman and published by Univ of California Press. This book was released on 1961 with total page 784 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Government Reports Announcements Index written by and published by . This book was released on 1983 with total page 940 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Multivariate Statistical Analysis written by Narayan C. Giri and published by CRC Press. This book was released on 2003-11-14 with total page 583 pages. Available in PDF, EPUB and Kindle. Book excerpt: Significantly revised and expanded, Multivariate Statistical Analysis, Second Edition addresses several added topics related to the properties and characterization of symmetric distributions, elliptically symmetric multivariate distributions, singular symmetric distributions, estimation of covariance matrices, tests of mean against one-sided altern
