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Shrinkage Estimation
William E. Strawderman (Gebundene Ausgabe, Englisch)
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Beschreibung
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. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
06.12.2018
Sprache
Englisch
EAN
9783030021849
Herausgeber
Springer International Publishing
Serien- oder Bandtitel
Springer Series in Statistics
Sonderedition
Nein
Autor
William E. Strawderman
Seitenanzahl
333
Auflage
1st edition 2018
Einbandart
Gebundene Ausgabe
Schlagwörter
Minimax Estimation, Bayes Estimation, Shrinkage Estimation, Multivariate Statistics, Spherical Symmetry, Decision Theory, Mathematical Statistics
Thema-Inhalt
PBT - Wahrscheinlichkeitsrechnung und Statistik
PBTB - Bayesianische Inferenz
Höhe
235 mm
Breite
15.5 cm
Hersteller: Springer, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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