Sure explained variability and independence screening

ABSTRACT

In the era of Big Data, extracting the most important exploratory variables available in ultrahigh-dimensional data plays a key role in scientific researches. Existing researches have been mainly focusing on applying the extracted exploratory variables to describe the central tendency of their related response variables. For a response variable, its variability characteristic is as much important as the central tendency in statistical inference. This paper focuses on the variability and proposes a new model-free feature screening approach: sure explained variability and independence screening (SEVIS). The core of SEVIS is to take the advantage of recently proposed asymmetric and nonlinear generalised measures of correlation in the screening. Under some mild conditions, the paper shows that SEVIS not only possesses desired sure screening property and ranking consistency property, but also is a computational convenient variable selection method to deal with ultrahigh-dimensional data sets with more features than observations. The superior performance of SEVIS, compared with existing model-free methods, is illustrated in extensive simulations. A real example in ultrahigh-dimensional variable selection demonstrates that the variables selected by SEVIS better explain not only the response variables, but also the variables selected by other methods.

KEYWORDS:

• Feature screening
• sure screening property
• generalised measures of correlation
• nonparametric inference
• model-free approach

Acknowledgments

The authors thank the editor, associate editor, two anonymous referees for their valuable comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Min Chen's work is partially supported by National Natural Science Foundation of China grants (nos. 11371345, 11690014). Zhao Chen's work is partially supported by National Natural Science Foundation of China grants (no. 11690015). Zhengjun Zhang's work is partially supported by NSF-DMS-1505367 and NSF-CMMI-1536978.