Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Optimal change-point estimation from indirect observations


Code(s) de Classification MSC:

Résumé: We study nonparametric change-point estimation from indirect noisy observations. Focusing on the white noise convolution model, we consider two classes of functions that are smooth apart from the change-point. We establish lower bounds on the minimax risk in estimating the change-point and develop rate optimal estimation procedures. The results demonstrate that the best achievable rates of convergence are determined both by smoothness of the function away from the change-point and by the degree of ill-posedness of the convolution operator. Optimality is obtained by introducing a new technique that involves as a key element detection of zero crossings of an estimate of the properly smoothed second derivative of the underlying function.

Mots Clés: change-point estimation ; deconvolution ; minimax risk ; ill--posedness ; probe functional ; optimal rates of convergence

Date: 2004-09-28

Prépublication numéro: PMA-939