• Bernoulli
  • Volume 22, Number 2 (2016), 1093-1112.

Behavior of R-estimators under measurement errors

Jana Jurečková, Hira L. Koul, Radim Navrátil, and Jan Picek

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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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Bernoulli, Volume 22, Number 2 (2016), 1093-1112.

Received: February 2014
Revised: October 2014
First available in Project Euclid: 9 November 2015

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Zentralblatt MATH identifier

contiguity linear rank statistic linear regression model local asymptotic bias measurement error R-estimate


Jurečková, Jana; Koul, Hira L.; Navrátil, Radim; Picek, Jan. Behavior of R-estimators under measurement errors. Bernoulli 22 (2016), no. 2, 1093--1112. doi:10.3150/14-BEJ687.

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