Generalized profile LSE in varying-coefficient partially linear models with measurement errors

This paper is concerned with the estimating problem of a semiparametric varying-coefficient partially linear errors-in-variables model Y _i = X _i ^t β + Z _i ^t α(U _i) + e{open} _i,W_i = X _i + ζ _i, i = 1,..., n. Due to measurement errors, the usual profile least square estimator of the parametric component, local polynomial estimator of the nonparametric component and profile least squares based estimator of the error variance are biased and inconsistent. By taking the measurement errors into account we propose a generalized profile least squares estimator for the parametric component and show it is consistent and asymptotically normal. Correspondingly, the consistent estimation of the nonparametric component and error variance are proposed as well. These results may be used to make asymptotically valid statistical inferences. Some simulation studies are conducted to illustrate the finite sample performance of these proposed estimations.