Multivariate Empirical Bayes and Estimation of Covariance Matrices

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Publisher :
ISBN 13 :
Total Pages : 21 pages
Book Rating : 4.:/5 (17 download)

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Book Synopsis Multivariate Empirical Bayes and Estimation of Covariance Matrices by : Bradley Efron

Download or read book Multivariate Empirical Bayes and Estimation of Covariance Matrices written by Bradley Efron and published by . This book was released on 1974 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of estimating a covariance matrix in the standard multivariate normal situation is considered. The loss function is one obtained naturally from the problem of estimating several normal mean vectors in an empirical Bayes Situation. Estimators which dominate any constant multiple of the sample covariance matrix are presented. These estimators work by shrinking the sample eigenvalues toward a central value, in much the same way as the James-Stein estimator for a mean vector shrinks the maximum likelihood estimators toward a common value.

Multivariate Empirical Bayes and Estimation of Covariance Matrices

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Publisher :
ISBN 13 :
Total Pages : 35 pages
Book Rating : 4.:/5 (632 download)

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Book Synopsis Multivariate Empirical Bayes and Estimation of Covariance Matrices by : Rand Corporation

Download or read book Multivariate Empirical Bayes and Estimation of Covariance Matrices written by Rand Corporation and published by . This book was released on 1970 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Empirical Bayes Estimation of the Mean in a Multivariate Normal Distribution

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ISBN 13 :
Total Pages : 36 pages
Book Rating : 4.3/5 (9 download)

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Book Synopsis Empirical Bayes Estimation of the Mean in a Multivariate Normal Distribution by : S. James Press

Download or read book Empirical Bayes Estimation of the Mean in a Multivariate Normal Distribution written by S. James Press and published by . This book was released on 1986 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This Note, reprinted from [Communications in Statistics, Theory and Methods], Vol. 15(7), 1986, considers the problem of estimating the mean vector of a multivariate normal distribution under a variety of assumed structures among the parameters of the sampling and prior distributions. The authors use a pragmatic approach. They adopt prior distributional families, assess hyperparameters, and adopt patterned mean and covariance structures when it is relatively simple to do so; alternatively, they use the sample data to estimate hyperparameters of prior distributions when assessment is a formidable task (e.g., when assessing parameters of multidimensional problems). James-Stein-like estimators result. In some cases, the authors have been able to show that the estimators proposed uniformly dominate the maximum likelihood estimators when measured with respect to quadratic loss functions."--Rand abstracts

Shrinkage Estimation for Mean and Covariance Matrices

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Publisher : Springer Nature
ISBN 13 : 9811515964
Total Pages : 119 pages
Book Rating : 4.8/5 (115 download)

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Book Synopsis Shrinkage Estimation for Mean and Covariance Matrices by : Hisayuki Tsukuma

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.

Multivariate Empirical Bayes Models for Replicated Microarray Time Course Data

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Publisher :
ISBN 13 :
Total Pages : 290 pages
Book Rating : 4.:/5 (35 download)

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Book Synopsis Multivariate Empirical Bayes Models for Replicated Microarray Time Course Data by : Yu Chuan Tai

Download or read book Multivariate Empirical Bayes Models for Replicated Microarray Time Course Data written by Yu Chuan Tai and published by . This book was released on 2005 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt:

High-Dimensional Covariance Estimation

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Publisher : John Wiley & Sons
ISBN 13 : 1118034295
Total Pages : 204 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis High-Dimensional Covariance Estimation by : Mohsen Pourahmadi

Download or read book High-Dimensional Covariance Estimation written by Mohsen Pourahmadi and published by John Wiley & Sons. This book was released on 2013-06-24 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Methods for estimating sparse and large covariance matrices Covariance and correlation matrices play fundamental roles in every aspect of the analysis of multivariate data collected from a variety of fields including business and economics, health care, engineering, and environmental and physical sciences. High-Dimensional Covariance Estimation provides accessible and comprehensive coverage of the classical and modern approaches for estimating covariance matrices as well as their applications to the rapidly developing areas lying at the intersection of statistics and machine learning. Recently, the classical sample covariance methodologies have been modified and improved upon to meet the needs of statisticians and researchers dealing with large correlated datasets. High-Dimensional Covariance Estimation focuses on the methodologies based on shrinkage, thresholding, and penalized likelihood with applications to Gaussian graphical models, prediction, and mean-variance portfolio management. The book relies heavily on regression-based ideas and interpretations to connect and unify many existing methods and algorithms for the task. High-Dimensional Covariance Estimation features chapters on: Data, Sparsity, and Regularization Regularizing the Eigenstructure Banding, Tapering, and Thresholding Covariance Matrices Sparse Gaussian Graphical Models Multivariate Regression The book is an ideal resource for researchers in statistics, mathematics, business and economics, computer sciences, and engineering, as well as a useful text or supplement for graduate-level courses in multivariate analysis, covariance estimation, statistical learning, and high-dimensional data analysis.

Empirical Bayes Estimates of Parameters from the Logistic Regression Model

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ISBN 13 :
Total Pages : 40 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Empirical Bayes Estimates of Parameters from the Logistic Regression Model by : Walter M. Houston

Download or read book Empirical Bayes Estimates of Parameters from the Logistic Regression Model written by Walter M. Houston and published by . This book was released on 1997 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Empirical Bayes Estimation for Unbalanced Multilevel Structural Equation Models Via the EM Algorithm

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Publisher :
ISBN 13 :
Total Pages : 196 pages
Book Rating : 4.3/5 (129 download)

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Book Synopsis Empirical Bayes Estimation for Unbalanced Multilevel Structural Equation Models Via the EM Algorithm by : See-Heyon Jo

Download or read book Empirical Bayes Estimation for Unbalanced Multilevel Structural Equation Models Via the EM Algorithm written by See-Heyon Jo and published by . This book was released on 1994 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Estimating Covariance Matrices

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ISBN 13 :
Total Pages : 246 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Estimating Covariance Matrices by : Wei-Liem Loh

Download or read book Estimating Covariance Matrices written by Wei-Liem Loh and published by . This book was released on 1988 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Bayesian Estimation of Multivariate Location Parameters

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ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)

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Book Synopsis Bayesian Estimation of Multivariate Location Parameters by : Ann Cohen Brandwein

Download or read book Bayesian Estimation of Multivariate Location Parameters 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: This paper presents an expository development of Bayesian estimation with substantial emphasis on exact results for the multivariate normal location models with respect to squared error loss. From the time Stein, in 1956, showed the inadmissibility of the best invariant estimator when sampling from a multivariate normal distribution in 3 or more dimensions, there has been an outpouring of improved estimators with a Bayesian flavor, encouraged largely by the connections between Bayes estimation, admissibility and minimaxity. In this chapter, we attempt to give a coherent presentation of numerous Bayesian results (proper, generalized, empirical) for this case. Generalizations for the location parameter of multivariate normal distributions with unknown covariance matrices and general quadratic loss are also presented.

Journal of Statistical Planning and Inference

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ISBN 13 :
Total Pages : 1216 pages
Book Rating : 4.3/5 (758 download)

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Book Synopsis Journal of Statistical Planning and Inference by : North-Holland Publishing Company

Download or read book Journal of Statistical Planning and Inference written by North-Holland Publishing Company and published by . This book was released on 2003 with total page 1216 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Theory of Preliminary Test and Stein-Type Estimation with Applications

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Publisher : John Wiley & Sons
ISBN 13 : 0471773743
Total Pages : 656 pages
Book Rating : 4.4/5 (717 download)

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Book Synopsis Theory of Preliminary Test and Stein-Type Estimation with Applications by : A. K. Md. Ehsanes Saleh

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

Multilevel Analysis of Educational Data

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Publisher : Elsevier
ISBN 13 : 1483295605
Total Pages : 367 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Multilevel Analysis of Educational Data by : R. Darrell Bock

Download or read book Multilevel Analysis of Educational Data written by R. Darrell Bock and published by Elsevier. This book was released on 2014-06-28 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multilevel Analysis of Educational Data - Bayesian methods - Empirical Bayes - Generalized least squares - Profile likelihoods - E-M algorithm - Fisher scoring procedures - Both educational and social science applications

An Introduction to Bayesian Analysis

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Publisher : Springer Science & Business Media
ISBN 13 : 0387354336
Total Pages : 356 pages
Book Rating : 4.3/5 (873 download)

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Book Synopsis An Introduction to Bayesian Analysis by : Jayanta K. Ghosh

Download or read book An Introduction to Bayesian Analysis written by Jayanta K. Ghosh and published by Springer Science & Business Media. This book was released on 2007-07-03 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a graduate-level textbook on Bayesian analysis blending modern Bayesian theory, methods, and applications. Starting from basic statistics, undergraduate calculus and linear algebra, ideas of both subjective and objective Bayesian analysis are developed to a level where real-life data can be analyzed using the current techniques of statistical computing. Advances in both low-dimensional and high-dimensional problems are covered, as well as important topics such as empirical Bayes and hierarchical Bayes methods and Markov chain Monte Carlo (MCMC) techniques. Many topics are at the cutting edge of statistical research. Solutions to common inference problems appear throughout the text along with discussion of what prior to choose. There is a discussion of elicitation of a subjective prior as well as the motivation, applicability, and limitations of objective priors. By way of important applications the book presents microarrays, nonparametric regression via wavelets as well as DMA mixtures of normals, and spatial analysis with illustrations using simulated and real data. Theoretical topics at the cutting edge include high-dimensional model selection and Intrinsic Bayes Factors, which the authors have successfully applied to geological mapping. The style is informal but clear. Asymptotics is used to supplement simulation or understand some aspects of the posterior.

A Rand Note

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ISBN 13 :
Total Pages : 36 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis A Rand Note by : Rand Corporation

Download or read book A Rand Note written by Rand Corporation and published by . This book was released on 1986 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nonlinear Models for Repeated Measurement Data

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Publisher : Routledge
ISBN 13 : 1351428152
Total Pages : 360 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Nonlinear Models for Repeated Measurement Data by : Marie Davidian

Download or read book Nonlinear Models for Repeated Measurement Data written by Marie Davidian and published by Routledge. This book was released on 2017-11-01 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear measurement data arise in a wide variety of biological and biomedical applications, such as longitudinal clinical trials, studies of drug kinetics and growth, and the analysis of assay and laboratory data. Nonlinear Models for Repeated Measurement Data provides the first unified development of methods and models for data of this type, with a detailed treatment of inference for the nonlinear mixed effects and its extensions. A particular strength of the book is the inclusion of several detailed case studies from the areas of population pharmacokinetics and pharmacodynamics, immunoassay and bioassay development and the analysis of growth curves.

Statistical Decision Theory and Bayesian Analysis

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Publisher : Springer Science & Business Media
ISBN 13 : 9780387960982
Total Pages : 648 pages
Book Rating : 4.9/5 (69 download)

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Book Synopsis Statistical Decision Theory and Bayesian Analysis by : James O. Berger

Download or read book Statistical Decision Theory and Bayesian Analysis written by James O. Berger and published by Springer Science & Business Media. This book was released on 1985-08-21 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The outstanding strengths of the book are its topic coverage, references, exposition, examples and problem sets... This book is an excellent addition to any mathematical statistician's library." -Bulletin of the American Mathematical Society In this new edition the author has added substantial material on Bayesian analysis, including lengthy new sections on such important topics as empirical and hierarchical Bayes analysis, Bayesian calculation, Bayesian communication, and group decision making. With these changes, the book can be used as a self-contained introduction to Bayesian analysis. In addition, much of the decision-theoretic portion of the text was updated, including new sections covering such modern topics as minimax multivariate (Stein) estimation.