Gradient Estimation for Ratios
P. W. Glynn, P. L’Ecuyer and M. Ades
Proceedings of the 1991 Winter Simulation Conference, 986-993 (1991)
The ratio estimation problem arises in many different applications settings. This paper is concerned with the interplay between gradient estimation and ratio estimation. Given unbiased estimators for the nnmerator and the denominator of the ratio, as well as their gradients, joint central-limit theorems for the ratio and its gradient are derived. The resulting confidence regions are of potential interest when optimizing such ratios numerically, or for sensitivity analysis with respect to parameters whose exact value is unknown. The paper also briefly discusses low-bias estimation for the gradient of a ratio.