Anisotropic multivariate deconvolution using projection on the Laguerre basis
Résumé
We investigate adaptive density estimation in the additive model Z = X + Y , where X and Y are independent d-dimensional random vectors with non-negative coordinates. Our goal is to recover the density of X from independent observations of Z, assuming the density of Y is known. In the d = 1 case, an estimation procedure using projection on the Laguerre basis have already been studied. We generalize this procedure in the multivariate case: we establish non-asymptotic upper bounds on the mean integrated squared error of the estimator and we derive convergence rates on anisotropic functional spaces. Moreover, we provide data-driven strategies for selecting the right projection space (for d = 1, we improve the previous projection procedure). We illustrate these procedures on simulated data, and in dimension d = 1 we compare our procedure with the previous adaptive projection procedure. December 9, 2019
Domaines
Statistiques [math.ST]Origine | Fichiers produits par l'(les) auteur(s) |
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