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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.
Estimation theory. --- Estimating techniques --- Least squares --- Mathematical statistics --- Stochastic processes --- Mathematical statistics. --- Statistics. --- Statistical Theory and Methods. --- Bayesian Inference. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Statistics .
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This book presents modern Bayesian analysis in a format that is accessible to researchers in the fields of ecology, wildlife biology, and natural resource management. Bayesian analysis has undergone a remarkable transformation since the early 1990s. Widespread adoption of Markov chain Monte Carlo techniques has made the Bayesian paradigm the viable alternative to classical statistical procedures for scientific inference. The Bayesian approach has a number of desirable qualities, three chief ones being: i) the mathematical procedure is always the same, allowing the analyst to concentrate on the scientific aspects of the problem; ii) historical information is readily used, when appropriate; and iii) hierarchical models are readily accommodated. This monograph contains numerous worked examples and the requisite computer programs. The latter are easily modified to meet new situations. A primer on probability distributions is also included because these form the basis of Bayesian inference. Researchers and graduate students in Ecology and Natural Resource Management will find this book a valuable reference.
Applied ecology. --- Statistics . --- Animal ecology. --- Forestry management. --- Applied Ecology. --- Statistics for Life Sciences, Medicine, Health Sciences. --- Animal Ecology. --- Forestry Management. --- Forest administration --- Forest plants --- Forest resource administration --- Forest resource management --- Forest stewardship --- Forest vegetation management --- Forestry management --- Forests and forestry --- Stewardship, Forest --- Vegetation management, Forest --- Ecosystem management --- Natural resources --- Animals --- Zoology --- Ecology --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Environmental protection --- Nature conservation --- Management --- Administration --- Control --- Applied ecology --- Bayesian statistical decision theory. --- Statistical methods. --- Bayes' solution --- Bayesian analysis --- Statistical decision
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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.
Statistical science --- Mathematical statistics --- Bayesian statistics --- statistiek --- statistisch onderzoek
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This book presents modern Bayesian analysis in a format that is accessible to researchers in the fields of ecology, wildlife biology, and natural resource management. Bayesian analysis has undergone a remarkable transformation since the early 1990s. Widespread adoption of Markov chain Monte Carlo techniques has made the Bayesian paradigm the viable alternative to classical statistical procedures for scientific inference. The Bayesian approach has a number of desirable qualities, three chief ones being: i) the mathematical procedure is always the same, allowing the analyst to concentrate on the scientific aspects of the problem; ii) historical information is readily used, when appropriate; and iii) hierarchical models are readily accommodated. This monograph contains numerous worked examples and the requisite computer programs. The latter are easily modified to meet new situations. A primer on probability distributions is also included because these form the basis of Bayesian inference. Researchers and graduate students in Ecology and Natural Resource Management will find this book a valuable reference.
Statistical science --- Animal ethology and ecology. Sociobiology --- Environmental protection. Environmental technology --- Forestry --- dierenecologie --- statistiek --- milieuzorg --- bossen
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This book is a collection of papers dedicated to the memory of Yehuda Vardi. Yehuda was the chair of the Department of Statistics of Rutgers University when he passed away unexpectedly on January 13, 2005.
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This book is a collection of papers dedicated to the memory of Yehuda Vardi. Yehuda was the chair of the Department of Statistics of Rutgers University when he passed away unexpectedly on January 13, 2005.
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This book is a collection of papers dedicated to the memory of Yehuda Vardi. Yehuda was the chair of the Department of Statistics of Rutgers University when he passed away unexpectedly on January 13, 2005.
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