Optimal Adaptive Estimation of A Quadratic Functional
Tony Cai and Mark Low
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Abstract:
Adaptive estimation of a quadratic functional over both Besov and
Lp balls is considered. A collection of
non-quadratic estimators are developed which have useful bias and
variance properties over individual Besov and Lp
balls. An adaptive procedure is then constructed based on penalized
maximization over this collection of non-quadratic estimators. This
procedure is shown to be optimally rate adaptive over the entire
range of Besov and Lp balls in the sense that
it attains certain constrained risk bounds.
- Paper:
pdf file.
- Other related papers:
Cai, T. & Low, M. (2005).
Non-quadratic estimators of a quadratic functional.
The Annals of Statistics 33, 2930-2956.Cai, T. & Low, M. (2006).
Adaptive confidence balls.
The Annals of Statistics 34, 202-228.