Deconvolution by simulation

Abstract

Given samples $(x_1,\ldots,x_m)$ and $(z_1, \ldots,z_n)$ which we believe are independent realizations of random variables $X$ and $Z$ respectively, where we further believe that $Z = X + Y$ with $Y$ independent of $X$, the problem is to estimate the distribution of $Y$. We present a new method for doing this, involving simulation. Experiments suggest that the method provides useful estimates.