Open Access
May 2016 Behavior of R-estimators under measurement errors
Jana Jurečková, Hira L. Koul, Radim Navrátil, Jan Picek
Bernoulli 22(2): 1093-1112 (May 2016). DOI: 10.3150/14-BEJ687


As was shown recently, the measurement errors in regressors affect only the power of the rank test, but not its critical region. Noting that, we study the effect of measurement errors on R-estimators in linear model. It is demonstrated that while an R-estimator admits a local asymptotic bias, its bias surprisingly depends only on the precision of measurements and does neither depend on the chosen rank test score-generating function nor on the regression model error distribution. The R-estimators are numerically illustrated and compared with the LSE and $L_{1}$ estimators in this situation.


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Jana Jurečková. Hira L. Koul. Radim Navrátil. Jan Picek. "Behavior of R-estimators under measurement errors." Bernoulli 22 (2) 1093 - 1112, May 2016.


Received: 1 February 2014; Revised: 1 October 2014; Published: May 2016
First available in Project Euclid: 9 November 2015

zbMATH: 06562306
MathSciNet: MR3449809
Digital Object Identifier: 10.3150/14-BEJ687

Keywords: contiguity , Linear rank statistic , linear regression model , local asymptotic bias , measurement error , R-estimate

Rights: Copyright © 2016 Bernoulli Society for Mathematical Statistics and Probability

Vol.22 • No. 2 • May 2016
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