Premium
Estimation of a multivariate mean with constraints on the norm
Author(s) -
Marchand Eric
Publication year - 1993
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315700
Subject(s) - equivariant map , estimator , mathematics , statistics , multivariate statistics , norm (philosophy) , estimation , multivariate normal distribution , invariant estimator , efficient estimator , minimum variance unbiased estimator , pure mathematics , economics , management , political science , law
Estimation of the mean θ of a spherical distribution with prior knowledge concerning the norm ||θ|| is considered. The best equivariant estimator is obtained for the local problem ||θ|| = λ 0 , and its risk is evaluated. This yields a sharp lower bound for the risk functions of a large class of estimators. The risk functions of the best equivariant estimator and the best linear estimator are compared under departures from the assumption ||θ|| = λ 0 .