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Asymptotic Relative Efficiency in Estimation

Asymptotic Relative Efficiency in EstimationRobert Serfling University of Texas at DallasOctober 2009 Prepared for forthcomingINTERNATIONAL ENCYCLOPEDIA OF STATISTICAL SCIENCES,to be published by SpringerAsymptotic Relative efficiency of two estimatorsFor statistical Estimation problems, it is typical and evendesirable that several reasonableestimators can arise for consideration. For example, the mean and median parameters ofa symmetric distribution coincide, and so thesample meanand thesample medianbecomecompeting estimators of the point of is preferred? By what criteria shallwe make a choice?One natural and time-honored approach is simply to compare the sample sizes at whichtwo competing estimators meet a given standard of performance. This depends upon thechosen measure of performance and upon the particular population make the discussion of sample mean versus sample median more precise, consider adistribution functionFwith density functionfsymmetric about an unknown point tobe estimated.

Detailed discussion of estimation of point of symmetry Let us now discuss in detail the example treated above, with F a distribution with density

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