Optimal Adaptive Estimation of A Quadratic Functional
The Annals of Statistics 34, 2298-2325, (2006).

Tony Cai and Mark Low

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• Abstract: Adaptive estimation of a quadratic functional over both Besov and L_p balls is considered. A collection of non-quadratic estimators are developed which have useful bias and variance properties over individual Besov and L_p 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 L_p balls in the sense that it attains certain constrained risk bounds.

• Paper: pdf file.

• Other related paper:

  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.
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