Estimation for the convolution of several multidimensional densities
Résumé
This work is concerned with the problem of estimating the m-fold convolution of the densities of m independent random vectors. Two nonparametric estimators are proposed, a kernel and a projection estimator, and their integrated quadratic risk is studied. We use Fourier analysis to bound the variance and consider standard Sobolev classes to discuss the convergence rates for the kernel estimator. In addition, we propose a bandwidth selection method for the kernel estimator and a study model selection for the projection estimator. Finally, we illustrate the results in simulation experiments.
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