On adaptive estimation of linear functionals

Abstract

Adaptive estimation of linear functionals over a collection of parameter spaces is considered. A between-class modulus of continuity, a geometric quantity, is shown to be instrumental in characterizing the degree of adaptability over two parameter spaces in the same way that the usual modulus of continuity captures the minimax difficulty of estimation over a single parameter space. A general construction of optimally adaptive estimators based on an ordered modulus of continuity is given. The results are complemented by several illustrative examples.

Published at http://dx.doi.org/10.1214/009053605000000633 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (3)

• An adaptation theory for nonparametric confidence intervals
• Minimax estimation of linear functionals over nonconvex parameter spaces
• Statistical properties of the method of regularization with periodic Gaussian reproducing kernel

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• Near-Optimal Recovery of Linear and N-Convex Functions on Unions of Convex Sets