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统计学前沿系列学术讲座--Concordance Measure-based Feature Screening and Variable Selection
时间  Datetime
2017-06-30 10:00 — 11:00 
地点  Venue
Middle Lecture Room
报告人  Speaker
林华珍
单位  Affiliation
西南财经大学统计学院教授
邀请人  Host
刘卫东
报告摘要  Abstract

The $C$-statistic, measuring the rank concordance between predictors and outcomes, has become a standard metric of predictive accuracy and  is therefore  a natural criterion for  variable screening and selection. However, as the $C$-statistic is a step function, its optimization requires brute-force search, prohibiting its direct usage in the presence of high-dimensional predictors. We develop a smoothed version of the $C$-statistic to facilitate variable screening and selection. Specifically, we propose a smoothed $C$-statistic sure screening (C-SS) method for screening ultrahigh-dimensional data, and a penalized  $C$-statistic (PSC)  variable selection method for regularized modeling  based on the screening results. We have shown that these two coherent procedures form an integrated framework for screening and variable selection: the C-SS possesses the sure screening property, and the PSC possesses the oracle property. Specifically, the PSC achieves the oracle property if $m_n = o( n^{1/4})$, where $m_n$ is the cardinality of the set of predictors captured by the C-SS. Our extensive simulations reveal that, compared to existing procedures, our proposal is more robust and efficient. Our procedure has been applied to analyze a multiple myeloma study, and has identified several novel genes that can predict patients response to treatment.