The Annals of Statistics

Estimates of Location: A Large Deviation Comparison

Gerald L. Sievers

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Abstract

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.

Article information

Source
Ann. Statist., Volume 6, Number 3 (1978), 610-618.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176344205

Digital Object Identifier
doi:10.1214/aos/1176344205

Mathematical Reviews number (MathSciNet)
MR494631

Zentralblatt MATH identifier
0395.62034

JSTOR
links.jstor.org

Subjects
Primary: 62G35: Robustness
Secondary: 60F10: Large deviations 62G20: Asymptotic properties

Keywords
Location parameter large deviations asymptotic efficiency $M$-estimates

Citation

Sievers, Gerald L. Estimates of Location: A Large Deviation Comparison. Ann. Statist. 6 (1978), no. 3, 610--618. doi:10.1214/aos/1176344205. https://projecteuclid.org/euclid.aos/1176344205


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