Nonlinearly Smoothed EM Density Estimation with Automated Smoothing Parameter Selection for Nonparametric Deconvolution Problems

We study a nonparametric deconvolution density estimation problem. The estimator is obtained by an EM algorithm for a smoothed maximum likelihood estimation problem, which has a unique continuous solution. We present an implementation of the procedure incorporating a data-driven discrepancy principle for selecting the smoothing parameter. Simulations illustrate the good properties of the resulting estimator when the unknown distribution is smooth and has regularly varying thin tails. Comparisons with a Fourier kernel deconvolution method are made for the case of normal noise. We show that under mild smoothness conditions, the estimator based on the data-driven smoothing parameter is strongly consistent.