Sparsity identification for high-dimensional partially linear model with measurement error

ABSTRACT

In this article, we studied the identification of significant predictors in partially linear model in which some regressors are contaminated with random errors. Moreover, the dimension of parametric component is divergent and the regression coefficients are sparse. We applied difference technique to remove the nonparametric component for circumventing the selection of bandwidth, and constructed a bias-corrected shrinking estimator for the coefficient by using smoothly clipped absolute deviation (SCAD) penalty. Then, we derived the estimating and selecting consistency and established the asymptotic distribution for the identified significant estimators. Finally, Monte Carlo studies illustrate the performance of our approach.

KEYWORDS:

• High-dimensional data
• Measurement error
• Oracle property
• Variable selection

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62G08
• Second 62J02

Funding

Haibing Zhao’s work was supported by a grant from the National Natural Science Foundation of China (NSFC, no. 11471204) and Rui Li’s work was sponsored by grants from the National Statistical Science Research Project (no. 2016LZ22] and Shanghai Pujiang Program (no. 16PJC042).