Unified mean-variance feature screening for ultrahigh-dimensional regression

Liming Wang, Xingxiang Li (), Xiaoqing Wang and Peng Lai
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Liming Wang: Nanjing University of Finance and Economics Hongshan College
Xingxiang Li: Xi’an Jiaotong University
Xiaoqing Wang: Nanjing University of Finance and Economics
Peng Lai: Nanjing University of Information Science and Technology

Computational Statistics, 2022, vol. 37, issue 4, No 13, 1887-1918

Abstract: Abstract Feature screening is a popular and efficient statistical technique in processing ultrahigh-dimensional data. When a regression model consists both categorical and continuous predictors, a unified feature screening procedure is needed. Thus, we propose a unified mean-variance sure independence screening (UMV-SIS) for this setup. The mean-variance (MV), an effective utility to measure the dependence between two random variables, is widely used in feature screening for discriminant analysis. In this paper, we advocate using the kernel smoothing method to estimate MV between two continuous variables, thereby extending it to screen categorical and continuous predictors simultaneously. Besides the uniformity for screening, UMV-SIS is a model-free procedure without any specification of a regression model; this broadens the scope of its application. In theory, we show that the UMV-SIS procedure has the sure screening and ranking consistency properties under mild conditions. To solve some difficulties in marginal feature screening for linear model and further enhance the screening performance of our proposed method, an iterative UMV-SIS procedure is developed. The promising performances of the new method are supported by extensive numerical examples.

Keywords: Ultrahigh-dimensional data; Mean-variance; Kernel smoothing estimate; Unified marginal utility; Sure screening property (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s00180-021-01184-2

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