Partially Linear Models with Generalized Measurement Errors and Diverging Number of Parameters

We consider partially linear models in which the linear covariate contains measurement errors, but instead an observed surrogate that is linearly related to the unobserved covariate. Moreover, the dimension of unobserved covariate diverges with the sample size. We propose an estimation procedure and establish the consistency and asymptotic normality property of estimate. The rate of the divergent dimension is also investigated. A simulation study and a real data are carried out to illustrate the usefulness of the proposed method.