Date of this Version
The Annals of Statistics
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.
adaptive estimation, between-class modulus of continuity, cost of adaptation, linear functional, ordered modulus of continuity, white noise model
Cai, T., & Low, M. G. (2005). On Adaptive Estimation of Linear Functionals. The Annals of Statistics, 33 (5), 2311-2343. http://dx.doi.org/10.1214/009053605000000633
Date Posted: 27 November 2017
This document has been peer reviewed.