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Variable selection for partially linear models via partial correlation.

ABSTRACT: The partially linear model (PLM) is a useful semiparametric extension of the linear model that has been well studied in the statistical literature. This paper proposes a variable selection procedure for the PLM with ultrahigh dimensional predictors. The proposed method is different from the existing penalized least squares procedure in that it relies on partial correlation between the partial residuals of the response and the predictors. We systematically study the theoretical properties of the proposed procedure and prove its model consistency property. We further establish the root-n convergence of the estimator of the regression coefficients and the asymptotic normality of the estimate of the baseline function. We conduct Monte Carlo simulations to examine the finite-sample performance of the proposed procedure and illustrate the proposed method with a real data example.

SUBMITTER: Liu J

PROVIDER: S-EPMC6555488 | biostudies-literature | 2018 Sep

REPOSITORIES: biostudies-literature

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Variable selection for partially linear models via partial correlation.

Liu Jingyuan J Lou Lejia L Li Runze R

Journal of multivariate analysis 20180620

The partially linear model (PLM) is a useful semiparametric extension of the linear model that has been well studied in the statistical literature. This paper proposes a variable selection procedure for the PLM with ultrahigh dimensional predictors. The proposed method is different from the existing penalized least squares procedure in that it relies on partial correlation between the partial residuals of the response and the predictors. We systematically study the theoretical properties of the ...[more]

PMID: 31182883

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