FUNCTIONAL ESTIMATION WITH RESPECT TO A THRESHOLD PARAMETER VIA DYNAMIC SPLIT-AND-MERGE

We consider a class of stochastic models for which the performance mea sure is defined as a mathematical expectation that depends on a parame ter theta, say alpha(theta)), and we are interested in constructing es timators of ct in functional form (i.e., entire functions of theta), w hich can be computed from a single simulation experiment. We focus on the case when theta is a continuous parameter, and also consider estim ation of the derivative alpha'(theta). One approach for doing that, wh en theta is a parameter of the probability law that governs the system , is based on the use of likelihood ratios and score functions. In thi s paper, we study a different approach, called split-and-merge, for th e case where theta is a threshold parameter. This approach can be view ed as a practical way of running parallel simulations at an infinite n umber of values of theta, with common random numbers. We give several examples showing how different kinds of parameters such as the arrival rate in a queue, the probability that an arriving customer be of a gi ven type, a scale parameter of a service time distribution, and so on, can be turned into threshold parameters. We also discuss implementati on issues.