Variable selection for high dimensional partially linear varying coe cient errors-in-variables models

In this paper, we consider variable selection procedure for the high dimensional partially linear varying coeffcient models where the parametric part covariates are measured with additive errors. The penalized bias-corrected profile least squares estimators are conducted, and their asymptotic properties are also studied under some regularity conditions. The rate of convergence and the asymptotic normality of the resulting estimates are established. We further demonstrate that, with proper choices of the penalty functions and the regularization parameter, the resulting estimates perform asymptotically as well as an oracle property. Choice of smoothing parameters is also discussed. Finite sample performance of the proposed variable selection procedures is assessed by Monte Carlo simulation studies.

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