Estimation of a density in a simulation model

Abstract

The problem of estimating density in a simulation model is considered. Given a value of an -valued random input parameter X, the value of a real-valued random variable is computed. Here is a function which measures the quality of a technical system with input X. It is assumed that X and Y have densities. Given a sample of , 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 -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.

Keywords:

• density estimation
• -error
• nonparametric regression
• consistency
• rate of convergence

AMS Subject Classifications:

• Primary: 62G07
• Secondary: 62G20

Acknowledgments

The authors would like to thank the associate editor and two anonymous referees for many very valuable comments, which helped to improve the manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The authors would like to thank the German Research Foundation (DFG) for funding this project within the Collaborative Research Center 805.