On adaptive estimation of linear functionals
The Annals of Statistics · 2005 · Volume 33 · Issue 5
DOI: 10.1214/009053605000000633
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.
Keywords
62F12, 62F35, 62G99, 62M99, adaptive estimation, between-class modulus of continuity, cost of adaptation, linear functional, ordered modulus of continuity, White noise model
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