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May, 1978 Estimates of Location: A Large Deviation Comparison
Gerald L. Sievers
Ann. Statist. 6(3): 610-618 (May, 1978). DOI: 10.1214/aos/1176344205


This paper considers the estimation of a location parameter $\theta$ in a one-sample problem. The asymptotic performance of a sequence of estimates $\{T_n\}$ is measured by the exponential rate of convergence to 0 of $\max \{P_\theta(T_n < \theta - a), P_\theta(T_n > \theta + a)\}, \text{say} e(a).$ This measure of asymptotic performance is equivalent to one considered by Bahadur (1967). The optimal value of $e(a)$ is given for translation invariant estimates. Some computational methods are reviewed for determining $e(a)$ for a general class of estimates which includes $M$-estimates, rank estimates and Hodges-Lehmann estimates. Finally, some numerical work is presented on the asymptotic efficiencies of some standard estimates of location for normal, logistic and double exponential models.


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Gerald L. Sievers. "Estimates of Location: A Large Deviation Comparison." Ann. Statist. 6 (3) 610 - 618, May, 1978.


Published: May, 1978
First available in Project Euclid: 12 April 2007

zbMATH: 0395.62034
MathSciNet: MR494631
Digital Object Identifier: 10.1214/aos/1176344205

Primary: 62G35
Secondary: 60F10 , 62G20

Keywords: $M$-estimates , Asymptotic efficiency , large deviations , location parameter

Rights: Copyright © 1978 Institute of Mathematical Statistics


Vol.6 • No. 3 • May, 1978
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