An Overview of Derivative Estimation

We explain the main techniques for estimating derivatives by simulation and survey the most recent developments in that area. In particular, we discuss perturbation analysis (PA), likelihood ratios (LR), weak derivatives (WD), finite differences (FD), and many of their variants. We also mention some other approaches. Our discussion emphasizes the relationships between the methods. For that purpose, all of them are presented in the same framework, which is based on L'Ecuyer (1990). 1. INTRODUCTION Simulation is a popular tool for estimating the expected (average) performance measure of a complex stochastic system. Various statistical techniques have been develop ed in that context. Estimating the derivative or sensitivity of such an expectation certainly looks more difficult, but is nevertheless important for many practical applications. For example, let ` be a real-valued (continuous) parameter and suppose that the performance measure of interest depends on ` either directly, or indi..