Behavior of R-estimators under measurement errors

TL;DR

This paper investigates how measurement errors influence R-estimators in linear models, revealing that their bias depends solely on measurement precision and not on other factors, with numerical comparisons to LSE and L1 estimators.

Contribution

It provides a novel analysis showing R-estimators' bias depends only on measurement precision, regardless of the score function or error distribution.

Findings

R-estimators have a local asymptotic bias influenced only by measurement accuracy.

Numerical comparisons show R-estimators' performance relative to LSE and L1 estimators.

Bias of R-estimators is unaffected by the choice of score-generating function.

Abstract

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.