Deconvolution Kernel Density Estimation

Abstract

We consider nonparametric estimation of the density of a variable which is observed with an independent additive noise of known distribution. We introduce the classical measurement error model and the deconvolution kernel density estimator in this errors-in-variables problem. The theoretical properties of this estimator depend on the smoothness of the error distribution. We introduce ordinary smooth and supersmooth errors and study the rates of convergence of the estimator for those two error types. We discuss the choice of the kernel function and the bandwidth and present some numerical issues that can be encountered when computing the estimator. We discuss several data-driven procedures of..