estimation performance of independant estimators

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Article #81

#81

From: Georg Wütschner
Date: Thu, 05 Jun 2003 17:01

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Hi folk,
I hope you allow me as an engineer a basic question:
a random variable (RV) takes on a certain value, which I have to
estimate. To this end I have a set of values, each of which was produced
by a given function of the RV plus noise.
Now an estimator E1 estimates the value of my RV with a certain variance V1.
An _independant_ second estimator E2 does the same, but has a much worse
set of values and therefore estimates with a bigger variance V2.

What would interest me is a statement on whether I can improve the
overall performance of my estimation by somehow combining the 2
estimators or if I allways make it worse. That is, is it possible to
achieve a variance lower than V2 when combining the result of E1 and
that of E2 (say weighted average or something more sophisticated)??
Can this wanted relation between V1, V2 and Vcomb. be mathematically
expressed? What are the conditions/constrictions?

Maybe something which could point in the same direction was the so
called weather problem a friend told me of:
If one weather station states that tomorrow it will rain with a
probability of 60%, and a second, which operates which totally different
methods (->independent), predicts rain wiht 70% prob., then one can
somehow calulate that it will rain with a prob. of, say, 80% (higher
than the higher of the two)... any idea how this works?


Thanks a lot,

Georg

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Message-ID: <3EDF7781.4030100@unibw-muenchen.de>
Date: Thu, 05 Jun 2003 19:01:53 +0200
From: Georg Wütschner
 <georg.wuetschner@unibw-muenchen.de>
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