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.

Mots clés: laguerre basis; model selection; nonparametric density estimation; anisotropic multivariate projection estimator

Domaines: Statistiques [math.ST]

Florian Dussap. Anisotropic multivariate deconvolution using projection on the Laguerre basis. Journal of Statistical Planning and Inference, 2021, 215, pp.23-46. ⟨10.1016/j.jspi.2021.02.005⟩. ⟨hal-02400684v3⟩