On Adaptive Estimation

P. J. Bickel

doi:10.1214/aos/1176345863

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Home > Journals > Ann. Statist. > Volume 10 > Issue 3 > Article

September, 1982 On Adaptive Estimation

P. J. Bickel

Ann. Statist. 10(3): 647-671 (September, 1982). DOI: 10.1214/aos/1176345863

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Abstract

We simplify a general heuristic necessary condition of Stein's for adaptive estimation of a Euclidean parameter in the presence of an infinite dimensional shape nuisance parameter and other Euclidean nuisance parameters. We derive sufficient conditions and apply them in the construction of adaptive estimates for the parameters of linear models and multivariate elliptic distributions. We conclude with a review of issues in adaptive estimation.