I am estimating the quantity V1^2 / (V1-V2) where V1 > V2 are parameters estimated by the random variables S1 and S2, where S1 and S2 are a summary statistics from a sample.
The obvious estimator is S1^2 / (S1-S2) but that estimator has a heavy right tail because, although V1>V2, there is no guarantee that S1>S2. More formally, E(S1^2 /(S1-S2)) is undefined because of the possibility that the denominator is zero. This can be a real problem when V1-V2 is small.
I don't know if this is a common problem, but I'm wondering if there are standard tricks for modifying the estimator so that the heavy tails are less of a problem.