Estimation du coût quadratique quand certaines composantes du paramètre de position sont positives

Abstract

We consider the problem of estimating the quadratic loss ‖ δ − θ ‖ 2 of point estimators δ of a location parameter θ = ( θ 1 , … , θ p ) for family of symmetric distributions with known scale parameter, when a subset of the components of θ are restricted to be nonnegative and when a residual vector U is available. In the normal case, we give a class of estimators λ 0 ( X ) + h ( X ) which dominate, under the usual quadratic loss, the unbiased estimator λ 0 of ‖ δ − θ ‖ 2 . In the general case when the vector ( X , U ) has a spherically symmetric distribution around ( θ , 0 ) , we give a class of estimators of the form λ 0 ( X ) + ‖ U ‖ 4 h ( X ) .