The Annals of Statistics

On Adaptive Estimation

P. J. Bickel

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 10, Number 3 (1982), 647-671.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345863

Digital Object Identifier
doi:10.1214/aos/1176345863

Mathematical Reviews number (MathSciNet)
MR663424

Zentralblatt MATH identifier
0489.62033

JSTOR
links.jstor.org

Subjects
Primary: 62F20
Secondary: 62G20: Asymptotic properties

Keywords
Adaptation efficient estimation linear models elliptic distributions

Citation

Bickel, P. J. On Adaptive Estimation. Ann. Statist. 10 (1982), no. 3, 647--671. doi:10.1214/aos/1176345863. https://projecteuclid.org/euclid.aos/1176345863


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