Variable Selection For Varying Coefficient Partially Linear Models With Measurement Errors

We consider variable selection for semiparameter varying-coefficient partially linear model Y= XTβ+α(V)Z+∈when X is measured with additive error. Estimators in the literature are biased when the measurement errors are ignored, thus may effect the result of the obtained variables.First the so-called correction-for-attenuation approach is used to correct the bias in the loss function caused by the measurement error. Then we employ the kernal estimation and penalized least squares—using the nonconvex penalized principle, to select variables and estimate coefficient simultaneously. We establish the rate of convergence of the result-ing estimate. With proper choice of regularization parameters, we show the asymptotic normality of the resulting estimate and further demonstrate that the proposed procedures perform as well as an oracle procedure.Given the " curse the dimension" of the kernal estimation when the dimension of the Z is large, We give another variable selection procedure, using the local linear estimate ofα(·) instead of the kernal estimate of Y, X given V, Z plus penalized least squares. Extensive simulation studies are conducted to examine the finite sample performance of the two proposed variable selection procedures.