An R-Estimator in the Errors in Variables Linear Regression Model

Abstract

This note develops an R estimator of the regression parameters in the errors in variables linear regression model, when the distributions of the vectors of covariates and measurement errors are known. The paper also contains the proof of the asymptotic uniform linearity of a sequence of a simple linear rank statistics based on the residuals of a class of nonlinear parametric regression models where covariates and regression errors are possibly dependent. This result in turn facilitates the proof of the asymptotic normality of the above mentioned R estimator in the errors in variables linear regression model. The Pitman’s asymptotic relative efficiency of this R estimator relative to the bias corrected least squares estimator is shown to increase to infinity as the measurement error variance increases to infinity at some Gaussian errors and covariate distributions.