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Estimation and variable selection in partial linear single index models with error-prone linear covariates. (English) Zbl 1367.62131
Summary: We study the estimation and variable selection for a partial linear single index model (PLSIM) when some linear covariates are not observed, but their ancillary variables are available. We use the semiparametric profile least-square based estimation procedure to estimate the parameters in the PLSIM after the calibrated error-prone covariates are obtained. Asymptotic normality for the estimators are established. We also employ the smoothly clipped absolute deviation (SCAD) penalty to select the relevant variables in the PLSIM. The resulting SCAD estimators are shown to be asymptotically normal and have the oracle property. Performance of our estimation procedure is illustrated through numerous simulations. The approach is further applied to a real data example.

MSC:
62G08 Nonparametric regression and quantile regression
62J07 Ridge regression; shrinkage estimators (Lasso)
62J12 Generalized linear models (logistic models)
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