Behavior of R-estimators under measurement errors. (English) Zbl 1388.62207

Summary: 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.


62J05 Linear regression; mixed models
62G20 Asymptotic properties of nonparametric inference
Full Text: DOI arXiv Euclid


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