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Biometrika 1976 63(3):680-681; doi:10.1093/biomet/63.3.680
© 1976 by Biometrika Trust
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Miscellanea

On estimating a symmetric distribution

DAVID HINKLEY

School of Statistics, University of Minnesota

One estimate of a symmetric location cumulative distribution function F{x - {theta}) is obtained by symmetrizing the sample cumulative distribution function with respect to the estimated centre of symmetry {theta}. We prove an earlier conjecture that if {theta} is asymptotically efficient, then the symmetrized estimated cumulative distribution function is uniformly superior to the sample distribution function.

Key Words: Efficiency • Estimation • Symmetric distribution


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