Anisotropic multivariate deconvolution using projection on the Laguerre basis

Florian Dussap (1)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5

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]

Florian Dussap. Anisotropic multivariate deconvolution using projection on the Laguerre basis. 2019. ⟨hal-02400684v1⟩