A kernel approach to estimating the density of a conditional expectation

Given uncertainty in the input model and parameters of a simulation study, the goal of the simulation study often becomes the estimation of a conditional expectation. The conditional expectation is expected performance conditional on the selected model and parameters. The distribution of this conditional expectation describes precisely, and concisely, the impact of input uncertainty on performance prediction. In this paper we estimate the density of a conditional expectation using ideas from the field of kernel density estimation. We present a result on asymptotically optimal rates of convergence and examine a number of numerical examples.