Gradient estimation for ratios

The authors consider the interplay between gradient estimation and ratio estimation. Given unbiased estimators for the numerator 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. Low-bias estimation for the gradient of a ratio is discussed