Randomly Weighted LAD-Estimation for Partially Linear Errors-in-Variables Models

The authors consider the partially linear model relating a response Y to predictors (x,T) with a mean function x(T)beta(0) + g(T) when the x's are measured with an additive error. The estimators of parameter beta(0) are derived by using the nearest neighbor-generalized randomly weighted least absolute deviation (LAD for short) method. The resulting estimator of the unknown vector beta(0) is shown to be consistent and asymptotically normal. In addition, the results facilitate the construction of confidence regions and the hypothesis testing for the unknown parameters. Extensive simulations are reported, showing that the proposed method works well in practical settings. The proposed methods are also applied to a data set from the study of an AIDS clinical trial group.