Estimation of a density in a simulation model

摘要

The problem of estimating density in a simulation model is considered. Given a value of an R-d-valued random input parameter X, the value of a real-valued random variable Y = m(X) is computed. Here m : R-d -> R is a function which measures the quality m(X) of a technical system with input X. It is assumed that X and Y have densities. Given a sample of (X, Y), the task is to estimate the density of Y. In a first step we estimate m and the density of X. Using these estimators we compute in a second step an estimator of the density of Y. Results concerning the L-1-consistency and the rate of convergence are proven and the finite sample behaviour of the estimators is illustrated by applying them to simulated and real data.