Estimating the density of a conditional expectation

Given uncertainty in the input model and parameters of a stochastic simulation study, the goal of the study often becomes the estimation of a conditional expectation. The conditional expectation is expected performance conditioned on the selected model and parameters. The density 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 show that our estimator converges under reasonable conditions and present results on optimal rates of convergence. We present two modifications of this estimator, a local estimator and a bias-corrected estimator. Convergence results are given for these estimators. We study the performance of our estimators on a number of test cases and a call center example in which the arrival process of customers is unknown.