Derivative Estimation with Finite Differences

Abstract

This article discusses the implementation of using finite differences to construct a confidence interval for a simulation estimator of the derivative of the steady-state distribution of a stochastic process. The quasi-independent procedure increases the simulation run length progressively until a certain number of essentially independent and identically distributed systematic samples are obtained. The author computes sample quantiles at certain grid points and constructs a histogram from those grid points. The derivative estimate is then computed from the histogram (i.e., the empirical distribution). An experimental performance evaluation demonstrates the validity of using this procedure to estimate the derivatives.