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Title: Estimating bounded mean vector in multivariate normal: the geometry of hartigan estimator
Other Titles: Estimação limitada do vetor de médias na normal multivariada: A geometria do estimador de Hartigan.
Authors: Gajo, Cristiane Alvarenga
Pereira, Leandro da Silva
Chaves, Lucas Monteiro
Souza, Devanil Jaques
Estimador de Bayes
Keywords: Multivariate normal
Convex sets
Uniform priors
Bayes estimator
Normal multivariada
Conjuntos convexos;
Priori uniforme
Estimador de Bayes
Issue Date: 1-Aug-2017
Publisher: Universidade Federal de Lavras
Citation: GAJO, C. A. et al. Estimating bounded mean vector in multivariate normal: the geometry of hartigan estimator. Revista Brasileira de Biometria, Lavras, v. 34, n. 2, p.304-316, jun. 2016.
Description: The problem on estimating a multivariate normal mean Np(θ; I) when the vector mean is bounded awaked interest practical and theoretical. Under such hypothesis it's possible to obtain estimators which dominate the sample mean estimator in relation to square loss. Generalizing previous results obtained, for univariate normal, J.A. Hartigan obtained, for multivariate normal with independent components, a Bayes estimator defined on a bounded closed convex set, with non-empty interior, which dominates the sample mean estimator. In this work, this result is presented in details for the case where the restriction set is a sphere centered at origin. A geometrical interpretation, useful to understand the phenomenon, is presented. Others estimators based on Gatsonis et. al. (1987) are proposed and the risks of all these estimators are compared through simulations, for the cases of dimensions p = 1 and p = 2.
Appears in Collections:Revista Brasileira de Biometria

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