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Article #84Re: estimation performance of independant estimators
From: Robert Israel
Date: Sun, 08 Jun 2003 20:53
Date: Sun, 08 Jun 2003 20:53
34 lines
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2180 bytes
In article <242be6f5.0306081036.7e5fcaf1@posting.google.com>, Ray Koopman <koopman@sfu.ca> wrote: >To avoid confusion with the expected value operator E, >call the estimates X1 and X2. Then we have >E(X1|RV) = RV, Var(X1|RV) = V1, >E(X2|RV) = RV, Var(X2|RV) = V2, >with X1|RV independent of X2|RV. >Let Xcomb = P1*X1 + P2*X2, where >P1 = (1/V1)/(1/V1 + 1/V2), >P2 = (1/V2)/(1/V1 + 1/V2). >Then E(Xcomb|RV) = RV, >and Var(Xcomb|RV) = V1*V2/(V1+V2), >which is less than both V1 and V2. >But note that V1 and V2 must be known >(as opposed to estimated). But using reasonably good estimates for V1 and V2 will probably still work. Say Xcomb = t X1 + (1-t) X2 Var(Xcomb|RV) = t^2 V1 + (1-t)^2 V2 which is less than both V1 and V2 as long as max(0,(V2-V1)/(V1+V2)) < t < min(1,(2 V2)/(V1+ V2)) Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada V6T 1Z2
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X-Google-Language: ENGLISH,ASCII-7-bit X-Google-Thread: f6df2,1c85a832432e36a9 X-Google-Attributes: gidf6df2,public X-Google-Thread: 10d632,1c85a832432e36a9 X-Google-Attributes: gid10d632,public X-Google-Thread: f6c01,1c85a832432e36a9 X-Google-Attributes: gidf6c01,public X-Google-Thread: 109d8a,1c85a832432e36a9 X-Google-Attributes: gid109d8a,public X-Google-ArrivalTime: 2003-06-08 13:53:58 PST Path: arc1-ca.pugleaf.net!archiver1.google.com!news1.google.com!newsfeed.stanford.edu!cyclone.bc.net!nntp.itservices.ubc.ca!not-for-mail From: israel@math.ubc.ca (Robert Israel) Newsgroups: sci.stat.math,sci.math,bln.net.statistik,bln.sci.mathematik Subject: Re: estimation performance of independant estimators Date: 8 Jun 2003 20:53:57 GMT Organization: ITServices, University of British Columbia Lines: 34 Message-ID: <bc07p5$me8$1@nntp.itservices.ubc.ca> References: <3EDF7781.4030100@unibw-muenchen.de> <242be6f5.0306081036.7e5fcaf1@posting.google.com> X-Trace: nntp.itservices.ubc.ca 1055105637 22984 137.82.36.63 (8 Jun 2003 20:53:57 GMT) X-Complaints-To: abuse@interchange.ubc.ca X-Newsreader: trn 4.0-test72 (19 April 1999)