Strawderman william e (10 Ergebnisse)
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Zustand: Sehr gut. Zustand: Sehr gut | Sprache: Englisch | Produktart: Bücher | This book provides a self-contained introduction of Stein/shrinkage estimation for the mean vector of a multivariate normal distribution. The book begins with a brief discussion of basic notions and results from decision theory such as admissibility,… minimaxity, and (generalized) Bayes estimation. It also presents Stein's unbiased risk estimator and the James-Stein estimator in the first chapter. In the following chapters, the authors consider estimation of the mean vector of a multivariate normal distribution in the known and unknown scale case when the covariance matrix is a multiple of the identity matrix and the loss is scaled squared error. The focus is on admissibility, inadmissibility, and minimaxity of (generalized) Bayes estimators, where particular attention is paid to the class of (generalized) Bayes estimators with respect to an extended Strawderman-type prior. For almost all results of this book, the authors present a self-contained proof. The book is helpful for researchers and graduate students in various fields requiring data analysis skills as well as in mathematical statistics.
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Zustand: Hervorragend. Zustand: Hervorragend | Sprache: Englisch | Produktart: Bücher | This book provides a self-contained introduction of Stein/shrinkage estimation for the mean vector of a multivariate normal distribution. The book begins with a brief discussion of basic notions and results from decision theory such as admiss…ibility, minimaxity, and (generalized) Bayes estimation. It also presents Stein's unbiased risk estimator and the James-Stein estimator in the first chapter. In the following chapters, the authors consider estimation of the mean vector of a multivariate normal distribution in the known and unknown scale case when the covariance matrix is a multiple of the identity matrix and the loss is scaled squared error. The focus is on admissibility, inadmissibility, and minimaxity of (generalized) Bayes estimators, where particular attention is paid to the class of (generalized) Bayes estimators with respect to an extended Strawderman-type prior. For almost all results of this book, the authors present a self-contained proof. The book is helpful for researchers and graduate students in various fields requiring data analysis skills as well as in mathematical statistics.
Shrinkage Estimation (Springer Series in Statistics)
Fourdrinier, Dominique; Strawderman, William E.; Wells, Martin T.
Sprache: Englisch
Verlag: Springer, 2018
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Shrinkage Estimation (Springer Series in Statistics)
Dominique Fourdrinier, William E. Strawderman, Martin T. Wells
Sprache: Englisch
Verlag: Springer International Publishing, 2018
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Gebundene Ausgabe. Zustand: Sehr gut. Gebraucht - Sehr gut SG - Ungelesenes Mängelexemplar, gestempelt, mit leichten Lagerspuren - 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.
Sprache: Englisch
Verlag: Springer, 2018
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Buch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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 es…timators 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.
Shrinkage Estimation
Fourdrinier, Dominique (Author)/ Strawderman, William E. (Author)/ Wells, Martin T. (Author)
Sprache: Englisch
Verlag: Springer, 2018
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Hardcover. Zustand: Brand New. 333 pages. 9.25x6.25x0.75 inches. In Stock.
