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Math Forum » Discussions » sci.math.* » sci.stat.math.independent

Topic: Taming a heavy-tailed estimator
Replies: 4   Last Post: Aug 24, 2012 11:06 AM

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paulvonhippel at yahoo

Posts: 72
Registered: 7/13/05
Taming a heavy-tailed estimator
Posted: Aug 13, 2012 8:43 AM
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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.

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