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A Note on Estimation from a Cauchy Sample

1964; Volume: 59; Issue: 306 Linguagem: Inglês

10.1080/01621459.1964.10482170

1537-274X

Thomas J. Rothenberg, Franklin M. Fisher, C.B. Tilanus,

Advanced Statistical Methods and Models

Abstract A class of estimators is proposed for the estimation of the center of the Cauchy distribution. Each estimator in the class is the arithmetic average of a central subset of the sample order statistics. Although the sample median is a member of the proposed class, it is not the most efficient. The average of roughly the middle quarter of the ordered sample has the lowest asymptotic variance.