In this paper, we consider a linear model in which the covariates are measured with errors. We propose a t-type corrected-loss estimation of the covariate effect, when the measurement error follows the Laplace distribution. The proposed estimator is asymptotically normal. In practical studies, some outliers that diminish the robustness of the estimation occur. Simulation studies show that the estimators are resistent to vertical outliers and an application of Six-Minute Walk test is presented to show that the proposed method performs well.
Keywords: Corrected-loss estimation; Error-in-variable model; Robust analysis; T-type.