Trace Pursuit: A General Framework for Model-Free Variable Selection

ABSTRACT

We propose trace pursuit for model-free variable selection under the sufficient dimension-reduction paradigm. Two distinct algorithms are proposed: stepwise trace pursuit and forward trace pursuit. Stepwise trace pursuit achieves selection consistency with fixed p. Forward trace pursuit can serve as an initial screening step to speed up the computation in the case of ultrahigh dimensionality. The screening consistency property of forward trace pursuit based on sliced inverse regression is established. Finite sample performances of trace pursuit and other model-free variable selection methods are compared through numerical studies. Supplementary materials for this article are available online.

KEYWORDS:

• Directional regression
• Selection consistency
• Sliced average variance estimation
• Sliced inverse regression
• Stepwise regression

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Supplementary Materials

The supplementary materials provide proofs of all the propositions and theorems.

Acknowledgment

The authors sincerely thank the associate editor and two anonymous referees for giving useful comments that led to a much-improved presentation of the article.

Funding

Yu's research was supported by National Natural Science Foundation of China Grant 11201151 and 11571111, the 111 Project B14019, the Program of Shanghai Subject Chief Scientist 14XD1401600, and the Shanghai Rising Star Program 16QA1401700. Dong's research was supported by the U.S. National Science Foundation Grant DMS-1106577. Zhu's research was supported by a grant from the Research Grants Council of Hong Kong, and an FRG grant from Hong Kong Baptist University.