| Abstract: | The authors consider the partially linear model relating a response$Y$ to predictors $(x,T)$ with a mean function $x^{rmT}beta_0+g(T)$ when the $x's$ are measured with an additive error.The estimators of parameter $beta_0$ are derived by using thenearest neighbor-generalized randomly weighted least absolutedeviation (LAD for short) method. The resulting estimator of theunknown vector $beta_{0}$ is shown to be consistent andasymptotically normal. In addition, the results facilitate theconstruction of confidence regions and the hypothesis testing forthe unknown parameters. Extensive simulations are reported, showingthat the proposed method works well in practical settings. Theproposed methods are also applied to a data set from the study of anAIDS clinical trial group. |
