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Profile forward regression screening for ultra-high dimensional semiparametric varying coefficient partially linear models. (English) Zbl 1360.62180
Summary: In this paper, we consider semiparametric varying coefficient partially linear models when the predictor variables of the linear part are ultra-high dimensional where the dimensionality grows exponentially with the sample size. We propose a profile forward regression (PFR) method to perform variable screening for ultra-high dimensional linear predictor variables. The proposed PFR algorithm can not only identify all relevant predictors consistently even for ultra-high semiparametric models including both nonparametric and parametric parts, but also possesses the screening consistency property. To determine whether or not to include the candidate predictor in the model of selected ones, we adopt an extended Bayesian information criterion (EBIC) to select the “best” candidate model. Simulation studies and a real data example are also carried out to assess the performance of the proposed method and to compare it with existing screening methods.

62G08 Nonparametric regression and quantile regression
62J02 General nonlinear regression
62H12 Estimation in multivariate analysis
62G20 Asymptotic properties of nonparametric inference
Full Text: DOI
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