Estimation of a multivariate mean with constraints on the norm | Zendy

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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 .

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