Projection correlation between scalar and vector variables and its use in feature screening with multi-response data

Abstract

In this article, we introduce a new methodology to perform feature screening for ultrahigh dimensional data with multivariate responses. Several extant screening procedures are available for multivariate responses, but they may be adversely affected by heavy-tailed observations or the dimension of multivariate responses. In order to attack these challenges, we first introduce a nonparametric coefficient, called projection correlation, to measure the departure of dependence between a scalar variable X and a vector variable $\mathbf{y}$. It takes values between zero and one, does not require any moment conditions on X and $\mathbf{y}$, and is zero if and only if X and $\mathbf{y}$ are independent. Based on its estimation that has desirable theoretical properties, such as algebraic simplicity and consistency, we present a novel sure independence screening procedure, which enjoys the desirable sure screening property. Numerical results demonstrate the effectiveness of the proposed procedure in comparison with the existing counterparts.

Keywords:

• Feature screening
• independence
• projection correlation
• ultrahigh dimensionality

Acknowledgments

We appreciate the constructive suggestions from the referees and the editors. Research is supported by grant No. 11901006 from the National Natural Science Foundation of China, by grant No. 1908085QA06 and grant No. 1908085MA20 from the Natural Science Foundation of Anhui Province and by grant No. 751811 from the Talent Foundation of Anhui Normal University.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Research is supported by grant No. 11901006 from the National Natural Science Foundation of China, by grant Nos. 1908085QA06 and 1908085MA20 from the Natural Science Foundation of Anhui Province and by grant No. 751811 from the Talent Foundation of Anhui Normal University.