Robust rank correlation based screening

By Gaorong Li, Heng Peng, Jun Zhang, Lixing Zhu. 2010

341 citations recorded by the source corpus.

Independence screening is a variable selection method that uses a ranking criterion to select significant variables, particularly for statistical models with nonpolynomial dimensionality or "large p, small n" paradigms when p can be as large as an exponential of the sample size n. In this paper we propose a robust rank correlation screening (RRCS) method to deal with ultra-high dimensional data. The new procedure is based on the Kendall \tau correlation coefficient between response and predictor variables rather than the Pearson correlation of existing methods. The new method has four desirable features compared with existing independence screening methods. First, the sure independence screening property can hold only under the existence of a second order moment of predictor variables, rather than exponential tails or alikeness, even when the number of predictor variables grows as fast as exponentially of the sample size. Second, it can be used to deal with semiparametric models such as transformation regression models and single-index models under monotonic constraint to the link function without involving nonparametric estimation even when there are nonparametric functions in the models. Third, the procedure can be largely used against outliers and influence points in the observations. Last, the use of indicator functions in rank correlation screening greatly simplifies the theoretical derivation due to the boundedness of the resulting statistics, compared with previous studies on variable screening. Simulations are carried out for comparisons with existing methods and a real data example is analyzed.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/34d899ec70c9fd0d0d105883f7b1863b11961ed4

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In Statistics and Probability

1. Chenlei Leng
2. Heng Peng
3. Xiangyu Wang
4. Ming-Yen Cheng
5. Hui Zou
6. Heng Lian
7. Cun-Hui Zhang
8. Toshio Honda

Citations in the corpus

• Challenges of Big Data Analysis (2013, neutral): “In addition, the authors of [91] utilized the distance correlation to conduct screening, [92] employed rank correlation and [28] proposed an iteratively screening and selection method.”
• High dimensional ordinary least squares projection for screening variables (2015, methodology): “As the SIS builds on marginal correlations between the response and the features, various extensions of correlation have been proposed to deal with more general cases (Hall and Miller, 2009; Zhu, et al., 2011; Li, Zhong, et al., 2012; Li, Peng, et al., 2012).”
• The fused Kolmogorov filter: A nonparametric model-free screening method (2014, methodology): “ the robustness of NIS by allowing heteroscedasticity in the model. Under such models, QA minimizes the check function instead of the squared error loss function to identify the important predictors. Li et al. (2012) propose using Kendall tau correlation to replace the usual Pearson correlation in m”
• A Simple Two-Sample Test in High Dimensions Based on L2-Norm (2020, background): “In regression, feature screening and selection, and dimension reduction are the mainstream approaches (Cheng and Wu 2013; Cook and Li 2002; Fan and Li 2001; Fan and Lv 2008; Fan and Peng 2004; Fan and Song 2010; Lv and Fan 2009; Li et al. 2012; Tibshirani 1996; Xia 2007, 2008).”
• Nonparametric independence screening and structure identification for ultra-high dimensional longitudinal data (2013, methodology): “In parametric settings, existing screening methods include the sure independence screening procedures [7, 10], the rank correlation screening procedure [17], and others.”