Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

 Messages: [ Previous | Next ]
 paulvonhippel at yahoo Posts: 72 Registered: 7/13/05
Taming a heavy-tailed estimator
Posted: Aug 13, 2012 8:43 AM

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.

Date Subject Author
8/13/12 paulvonhippel at yahoo
8/13/12 paulvonhippel at yahoo
8/13/12 Herman Rubin
8/14/12 David Jones
8/24/12 divergent.tseries@gmail.com