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Minimax Estimation Of Location Parameters For Spherically Symmetric Unimodal Distributions Under Quadratic Loss
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Book Synopsis Minimax Estimation of Location Parameters for Spherically Symmetric Unimodal Distributions Under Quadratic Loss by : Ann Cohen Brandwein
Download or read book Minimax Estimation of Location Parameters for Spherically Symmetric Unimodal Distributions Under Quadratic Loss written by Ann Cohen Brandwein and published by . This book was released on 2006 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt: Families of minimax estimators are found for the location parameter of a p-variate (pgt; or = 3) spherically symmetric unimodal(s.s.u.)distribution with respect to general quadratic loss. The estimators of James and Stein, Baranchik, Bock and Strawderman are all considered for this general problem. Specifically, when the loss is general quadratic loss given by L(delta,theta) = (delta - theta)'D(delta - theta) where D is a known pxp positive definite matrix, one main result, for one observation, X, on a multivariate s.s.u. distribution about theta, presents a class of minimax estimators whose risks dominate the risk of X, provided pgt; or = 3 and trace D gt; or equal 2dL where dL is the maximum eigenvalue of D. This class is given by Delta a,r(X)=(1-a(r(||X||2)/||X||2))X where 0lt; or = r(.)lt; or = 1, r(||X||2) is nondecreasing, r(||X||2)/||X||2 is nonincreasing, and 0lt;alt;(co/E(||X||-2)((traceD/dL)-2), where co=2p/((p+2)(p-2)) when pgt; or = 4 and co = .96 when p=3.
Book Synopsis Minimax Estimation of Location Parameters for Spherically Symmetric Distributions with Concave Loss by : Ann Cohen Brandwein
Download or read book Minimax Estimation of Location Parameters for Spherically Symmetric Distributions with Concave Loss written by Ann Cohen Brandwein and published by . This book was released on 2006 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: For p >4 and one observation X on a p-dimensional spherically symmetric distribution, minimax estimators of Theta whose risks are smaller than the risk of X (the best invariant estimator) are found when the loss is a nondecreasing concave function of quadratic loss. For n observations X1, X2, ... Xn, we have classes of minimax estimators which are better than the usual procedures, such as the best invariant estimator, X-bar, or a maximum likelihood estimator.
Book Synopsis Bayesian Thinking, Modeling and Computation by :
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
Book Synopsis Shrinkage Estimation by : Dominique Fourdrinier
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.
Book Synopsis Aspects of Multivariate Statistical Theory by : Robb J. Muirhead
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.
Book Synopsis Theory of Point Estimation by : Erich L. Lehmann
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".
Book Synopsis Advanced Econometric Theory by : John Chipman
Download or read book Advanced Econometric Theory written by John Chipman and published by Routledge. This book was released on 2013-03-01 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: When learning econometrics, what better way than to be taught by one of its masters. In this significant new volume, John Chipman, the eminence grise of econometrics, presents his classic lectures in econometric theory. Starting with the linear regression model, least squares, Gauss-Markov theory and the first principals of econometrics, this book guides the introductory student to an advanced stage of ability. The text covers multicollinearity and reduced-rank estimation, the treatment of linear restrictions and minimax estimation. Also included are chapters on the autocorrelation of residuals and simultaneous-equation estimation. By the end of the text, students will have a solid grounding in econometrics. Despite the frequent complexity of the subject matter, Chipman's clear explanations, concise prose and sharp analysis make this book stand out from others in the field. With mathematical rigor sharpened by a lifetime of econometric analysis, this significant volume is sure to become a seminal and indispensable text in this area.
Book Synopsis Contemporary Experimental Design, Multivariate Analysis and Data Mining by : Jianqing Fan
Download or read book Contemporary Experimental Design, Multivariate Analysis and Data Mining written by Jianqing Fan and published by Springer Nature. This book was released on 2020-05-22 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: The collection and analysis of data play an important role in many fields of science and technology, such as computational biology, quantitative finance, information engineering, machine learning, neuroscience, medicine, and the social sciences. Especially in the era of big data, researchers can easily collect data characterised by massive dimensions and complexity. In celebration of Professor Kai-Tai Fang’s 80th birthday, we present this book, which furthers new and exciting developments in modern statistical theories, methods and applications. The book features four review papers on Professor Fang’s numerous contributions to the fields of experimental design, multivariate analysis, data mining and education. It also contains twenty research articles contributed by prominent and active figures in their fields. The articles cover a wide range of important topics such as experimental design, multivariate analysis, data mining, hypothesis testing and statistical models.
Download or read book Bayes Theory written by J. A. Hartigan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on lectures given at Yale in 1971-1981 to students prepared with a course in measure-theoretic probability. It contains one technical innovation-probability distributions in which the total probability is infinite. Such improper distributions arise embarras singly frequently in Bayes theory, especially in establishing correspondences between Bayesian and Fisherian techniques. Infinite probabilities create interesting complications in defining conditional probability and limit concepts. The main results are theoretical, probabilistic conclusions derived from probabilistic assumptions. A useful theory requires rules for constructing and interpreting probabilities. Probabilities are computed from similarities, using a formalization of the idea that the future will probably be like the past. Probabilities are objectively derived from similarities, but similarities are sUbjective judgments of individuals. Of course the theorems remain true in any interpretation of probability that satisfies the formal axioms. My colleague David Potlard helped a lot, especially with Chapter 13. Dan Barry read proof. vii Contents CHAPTER 1 Theories of Probability 1. 0. Introduction 1 1. 1. Logical Theories: Laplace 1 1. 2. Logical Theories: Keynes and Jeffreys 2 1. 3. Empirical Theories: Von Mises 3 1. 4. Empirical Theories: Kolmogorov 5 1. 5. Empirical Theories: Falsifiable Models 5 1. 6. Subjective Theories: De Finetti 6 7 1. 7. Subjective Theories: Good 8 1. 8. All the Probabilities 10 1. 9. Infinite Axioms 11 1. 10. Probability and Similarity 1. 11. References 13 CHAPTER 2 Axioms 14 2. 0. Notation 14 2. 1. Probability Axioms 14 2. 2.
Book Synopsis Estimation and Inferential Statistics by : Pradip Kumar Sahu
Download or read book Estimation and Inferential Statistics written by Pradip Kumar Sahu and published by Springer. This book was released on 2015-11-03 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the meaning of statistical inference and estimation. Statistical inference is concerned with the problems of estimation of population parameters and testing hypotheses. Primarily aimed at undergraduate and postgraduate students of statistics, the book is also useful to professionals and researchers in statistical, medical, social and other disciplines. It discusses current methodological techniques used in statistics and related interdisciplinary areas. Every concept is supported with relevant research examples to help readers to find the most suitable application. Statistical tools have been presented by using real-life examples, removing the “fear factor” usually associated with this complex subject. The book will help readers to discover diverse perspectives of statistical theory followed by relevant worked-out examples. Keeping in mind the needs of readers, as well as constantly changing scenarios, the material is presented in an easy-to-understand form.
Book Synopsis Statistics in the 21st Century by : Adrian E. Raftery
Download or read book Statistics in the 21st Century written by Adrian E. Raftery and published by CRC Press. This book was released on 2001-07-09 with total page 571 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume discusses an important area of statistics and highlights the most important statistical advances. It is divided into four sections: statistics in the life and medical sciences, business and social science, the physical sciences and engineering, and theory and methods of statistics.
Book Synopsis Frontiers of Statistical Decision Making and Bayesian Analysis by : Ming-Hui Chen
Download or read book Frontiers of Statistical Decision Making and Bayesian Analysis written by Ming-Hui Chen and published by Springer Science & Business Media. This book was released on 2010-07-24 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: Research in Bayesian analysis and statistical decision theory is rapidly expanding and diversifying, making it increasingly more difficult for any single researcher to stay up to date on all current research frontiers. This book provides a review of current research challenges and opportunities. While the book can not exhaustively cover all current research areas, it does include some exemplary discussion of most research frontiers. Topics include objective Bayesian inference, shrinkage estimation and other decision based estimation, model selection and testing, nonparametric Bayes, the interface of Bayesian and frequentist inference, data mining and machine learning, methods for categorical and spatio-temporal data analysis and posterior simulation methods. Several major application areas are covered: computer models, Bayesian clinical trial design, epidemiology, phylogenetics, bioinformatics, climate modeling and applications in political science, finance and marketing. As a review of current research in Bayesian analysis the book presents a balance between theory and applications. The lack of a clear demarcation between theoretical and applied research is a reflection of the highly interdisciplinary and often applied nature of research in Bayesian statistics. The book is intended as an update for researchers in Bayesian statistics, including non-statisticians who make use of Bayesian inference to address substantive research questions in other fields. It would also be useful for graduate students and research scholars in statistics or biostatistics who wish to acquaint themselves with current research frontiers.
Book Synopsis Improved Estimation of Distribution Parameters: Stein-Type Estimators by : Kurt Hoffmann
Download or read book Improved Estimation of Distribution Parameters: Stein-Type Estimators written by Kurt Hoffmann and published by Springer. This book was released on 1992-02 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Minimax Estimation of the Parameter of the Maxwell Distribution Under Quadratic Loss Function by : Huda Abdullah
Download or read book Minimax Estimation of the Parameter of the Maxwell Distribution Under Quadratic Loss Function written by Huda Abdullah and published by . This book was released on 2016 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is concerned with the problem of finding the minimax estimators of the parameter of the Maxwell distribution (MW) for quadratic loss functions by applying the theorem of Lehmann [1950]. Through simulation study the performance of this method compared with the classical methods containing the Maximum Likelihood and moment Estimators with respect to Mean squared-errors (MSEs) .We reach to that the Minimax estimator with small positive values of c gives the best results, followed by the Maximum likelihood estimator.
Book Synopsis Statistical Theory and Method Abstracts by :
Download or read book Statistical Theory and Method Abstracts written by and published by . This book was released on 1979 with total page 1268 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stein Estimation for Spherically Symmetric Distributions by : Ann Cohen Brandwein
Download or read book Stein Estimation for Spherically Symmetric Distributions written by Ann Cohen Brandwein and published by . This book was released on 2016 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper reviews advances in Stein-type shrinkage estimation for spherically symmetric distributions. Some emphasis is placed on developing intuition as to why shrinkage should work in location problems whether the underlying population is normal or not. Considerable attention is devoted to generalizing the “Stein lemma” which underlies much of the theoretical development of improved minimax estimation for spherically symmetric distributions. A main focus is on distributional robustness results in cases where a residual vector is available to estimate an unknown scale parameter, and, in particular, in finding estimators which are simultaneously generalized Bayes and minimax over large classes of spherically symmetric distributions. Some attention is also given to the problem of estimating a location vector restricted to lie in a polyhedral cone.
Book Synopsis Applied Statistical Science III by : Mohammad Ahsanullah
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.
