ON ADAPTIVE WAVELET ESTIMATION OF A QUADRATIC FUNCTIONAL FROM A DECONVOLUTION PROBLEM

Christophe Chesneau (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

We consider the following situation: an unknown function f is observed in Gaussian white noise after convolution with a known function g. We wish to estimate the quadratic functional $\int f^2(t)dt$ from the observations. To reach this goal, we propose an adaptive estimator based on wavelet thresholding. We prove that it achieves near optimal rates of convergence under the mean squared error over a range of smoothness classes.

Mots clés: Deconvolution; Quadratic functionals; Adaptive curve estimation; Wavelets; Global thresholding

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Christophe Chesneau. ON ADAPTIVE WAVELET ESTIMATION OF A QUADRATIC FUNCTIONAL FROM A DECONVOLUTION PROBLEM. 2008. ⟨hal-00174239v4⟩