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Taming a heavytailed estimator
Posted:
Aug 13, 2012 8:43 AM


I am estimating the quantity V1^2 / (V1V2) 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 / (S1S2) but that estimator has a heavy right tail because, although V1>V2, there is no guarantee that S1>S2. More formally, E(S1^2 /(S1S2)) is undefined because of the possibility that the denominator is zero. This can be a real problem when V1V2 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.



