Groupe d’études et de recherche en analyse des décisions


Functional Estimation with Respect to a Threshold Parameter via Dynamic Split-and-Merge


We consider a class of stochastic models for which the performance measure is defined as a mathematical expectation that depends on a parameter , say (), and we are interested in constructing estimators of in functional form (i.e., entire functions of ), which can be computed from a single simulation experiment. We focus on the case where is a continuous parameter, and also consider estimation of the derivative '(). One approach for doing that, when is a parameter of the probability law that governs the system, is based on the use of likelihood ratios and score functions. In this paper, we study a different approach, called split-and-merge, for the case where is a threshold parameter. This approach can be viewed as a practical way of running parallel simulations at an infinite number of values of , 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 given type, a scale parameter of a service time distribution, and so on, can be turned into threshold parameters. We also discuss implementation issues.

, 32 pages