TY - JOUR
AU - GAJO, Cristiane Alvarenga
AU - PEREIRA, Leandro da Silva
AU - CHAVES, Lucas Monteiro
AU - SOUZA, Devanil Jaques
PY - 2016/06/28
Y2 - 2024/08/07
TI - ESTIMATING BOUNDED MEAN VECTOR IN MULTIVARIATE NORMAL: THE GEOMETRY OF HARTIGAN ESTIMATOR
JF - Brazilian Journal of Biometrics
JA - Braz. J. Biom.
VL - 34
IS - 2
SE - Articles
DO -
UR - http://www.biometria.ufla.br/index.php/BBJ/article/view/142
SP - 304-316
AB - <p>The problem on estimating a multivariate normal mean <em>N<sub>p</sub></em>(<em>θ</em>; <em>I</em>) 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 <em>p</em> = 1 and <em>p</em> = 2. </p>
ER -