Computing Wavelet Density Estimator For Stochastic Processes

: Let (X t ) be a stictly stationary stochastic process (in continuous or discrete time). We are to estimate the density f of X t on the basis of discrete observations (X i ); i = 1; :::; N using a "linear" wavelet estimator. For the continuous time process (X t ); 0 t T those observations are the result of a regular discretization of the continuous time trajectory. We provide an adaptive version of the algorithm, which adapts automatically to the regularity parameters of the density f . To compute the estimator we implement a fast algorithm (the whole effort to compute the estimate is order N log N for the sample size N ). Key-words: density estimation, adaptive minimax, wavelet estimators. (R'esum'e : tsvp) LSTA-Universit'e Paris VI, 75252 Paris Cedex 5 IRISA-Rennes, 35042 Rennes Cedex Centre National de la Recherche Scientifique Institut National de Recherche en Informatique (URA 227) Universite de Rennes 1 -- Insa de Rennes et en Automatique -- unite de recherche de Rennes ..