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September, 1994 Asymptotics of the Repeated Median Slope Estimator
Ola Hossjer, Peter J. Rousseeuw, Christophe Croux
Ann. Statist. 22(3): 1478-1501 (September, 1994). DOI: 10.1214/aos/1176325638

Abstract

The influence function is determined for (twice) repeated median estimators with arbitrary kernel functions, and more generally in the case where the two medians are replaced by a general class of estimators. Asymptotic normality is then established for the repeated median estimator of the slope parameter in simple linear regression. In this case the influence function is bounded. For bivariate Gaussian data the efficiency becomes $4/\pi^2 \approx 40.5{\tt \%},$ which is the square of the efficiency of the univariate median. The asymptotic results are compared with finite-sample efficiencies. It turns out that the convergence to the asymptotic behavior is extremely slow.

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Ola Hossjer. Peter J. Rousseeuw. Christophe Croux. "Asymptotics of the Repeated Median Slope Estimator." Ann. Statist. 22 (3) 1478 - 1501, September, 1994. https://doi.org/10.1214/aos/1176325638

Information

Published: September, 1994
First available in Project Euclid: 11 April 2007

zbMATH: 0817.62018
MathSciNet: MR1311985
Digital Object Identifier: 10.1214/aos/1176325638

Subjects:
Primary: 62F35
Secondary: 62J05

Rights: Copyright © 1994 Institute of Mathematical Statistics

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Vol.22 • No. 3 • September, 1994
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