Abstract
In the location estimation problem, translation equivariant estimators are considered. It is shown that under a mild regularity condition the distribution of such estimators is more spread out than a particular distribution which is defined in terms of the sample size and the density of the i.i.d. observations. Some consequences of this so-called spread-inequality are discussed, namely the Cramer-Rao inequality, an asymptotic minimax inequality and the efficiency of the maximum likelihood estimator in some nonregular cases.
Citation
Chris A. J. Klaassen. "Location Estimators and Spread." Ann. Statist. 12 (1) 311 - 321, March, 1984. https://doi.org/10.1214/aos/1176346409
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