With the rapid-growth-in-size scientific data in various disciplines, feature screening plays an important role to reduce the high-dimensionality to a moderate scale in many scientific fields. In this paper, we introduce a unified and robust model-free feature screening approach for high-dimensional survival data with censoring, which has several advantages: it is a model-free approach under a general model framework, and hence avoids the complication to specify an actual model form with huge number of candidate variables; under mild conditions without requiring the existence of any moment of the response, it enjoys the ranking consistency and sure screening properties in ultra-high dimension. In particular, we impose a conditional independence assumption of the response and the censoring variable given each covariate, instead of assuming the censoring variable is independent of the response and the covariates. Moreover, we also propose a more robust variant to the new procedure, which possesses desirable theoretical properties without any finite moment condition of the predictors and the response. The computation of the newly proposed methods does not require any complicated numerical optimization and it is fast and easy to implement. Extensive numerical studies demonstrate that the proposed methods perform competitively for various configurations. Application is illustrated with an analysis of a genetic data set.
feature screening random censoring robustness sure independence screening ultra-high dimension
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This work was supported by the Research Grant Council of Hong Kong (Grant Nos. 509413 and 14311916), Direct Grants for Research of The Chinese University of Hong Kong (Grant Nos. 3132754 and 4053235), the Natural Science Foundation of Jiangxi Province (Grant No. 20161BAB201024), the Key Science Fund Project of Jiangxi Province Eduction Department (Grant No. GJJ150439), the National Natural Science Foundation of China (Grant Nos. 11461029, 11601197 and 61562030) and the Canadian Institutes of Health Research (Grant No. 145546). The authors are grateful to the two reviewers for their insightful comments that lead to substantial improvements in the paper. The authors are also thankful to Professor Liping Zhu for his constructive comments.
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