Two approaches for estimating the gradient in functional form

Consider a stochastic model for which the performance measure is defined as a mathematical expectation which depends on a parameter /spl theta/. By using a likelihood ratio (i.e., a change of measure), it is often possible to construct an estimator of the performance measure in functional form, i.e., given as a function of /spl theta/, and computed from a single simulation run. It is also possible to obtain in functional form an estimator of the gradient with respect to /spl theta/. On way of doing that is to combine the likelihood ratio technique with a score function gradient estimator; another way is to combine it with a perturbation analysis gradient estimator. We compare and illustrate those two approaches.