1
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Chen LP. A note of feature screening via a rank-based coefficient of correlation. Biom J 2023:e2100373. [PMID: 37160692 DOI: 10.1002/bimj.202100373] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/24/2021] [Revised: 09/13/2022] [Accepted: 02/05/2023] [Indexed: 05/11/2023]
Abstract
Feature screening is a useful and popular tool to detect informative predictors for ultrahigh-dimensional data before developing statistical analysis or constructing statistical models. While a large body of feature screening procedures has been developed, most methods are restricted to examine either continuous or discrete responses. Moreover, even though many model-free feature screening methods have been proposed, additional assumptions are imposed in those methods to ensure their theoretical results. To address those difficulties and provide simple implementation, in this paper we extend the rank-based coefficient of correlation to develop a feature screening procedure. We show that this new screening criterion is able to deal with continuous and binary responses. Theoretically, the sure screening property is established to justify the proposed method. Simulation studies demonstrate that the predictors with nonlinear and oscillatory trajectories are successfully retained regardless of the distribution of the response. Finally, the proposed method is implemented to analyze two microarray datasets.
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Affiliation(s)
- Li-Pang Chen
- Department of Statistics, National Chengchi University, Taipei, Taiwan, ROC
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2
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Li X, Xu C. Feature Screening with Conditional Rank Utility for Big-data Classification. J Am Stat Assoc 2023. [DOI: 10.1080/01621459.2023.2195976] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/30/2023]
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3
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Cui H, Liu Y, Mao G, Zhang J. Model-free conditional screening for ultrahigh-dimensional survival data via conditional distance correlation. Biom J 2023; 65:e2200089. [PMID: 36526602 DOI: 10.1002/bimj.202200089] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2022] [Revised: 09/15/2022] [Accepted: 09/20/2022] [Indexed: 12/23/2022]
Abstract
How to select the active variables that have significant impact on the event of interest is a very important and meaningful problem in the statistical analysis of ultrahigh-dimensional data. In many applications, researchers often know that a certain set of covariates are active variables from some previous investigations and experiences. With the knowledge of the important prior knowledge of active variables, we propose a model-free conditional screening procedure for ultrahigh dimensional survival data based on conditional distance correlation. The proposed procedure can effectively detect the hidden active variables that are jointly important but are weakly correlated with the response. Moreover, it performs well when covariates are strongly correlated with each other. We establish the sure screening property and the ranking consistency of the proposed method and conduct extensive simulation studies, which suggests that the proposed procedure works well for practical situations. Then, we illustrate the new approach through a real dataset from the diffuse large-B-cell lymphoma study S1.
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Affiliation(s)
- Hengjian Cui
- School of Mathematical Sciences, Capital Normal University, Beijing, China
| | - Yanyan Liu
- School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei, China
| | - Guangcai Mao
- School of Mathematics and Statistics, Central China Normal University, Wuhan, Hubei, China
| | - Jing Zhang
- School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan, Hubei, China
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4
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Li T, Yu J, Meng C. Scalable model-free feature screening via sliced-Wasserstein dependency. J Comput Graph Stat 2023. [DOI: 10.1080/10618600.2023.2183213] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/25/2023]
Affiliation(s)
- Tao Li
- Center for Applied Statistics, Institute of Statistics and Big Data, Renmin University of China
| | - Jun Yu
- School of Mathematics and Statistics, Beijing Institute of Technology
| | - Cheng Meng
- Center for Applied Statistics, Institute of Statistics and Big Data, Renmin University of China
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5
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Li L, Ke C, Yin X, Yu Z. Generalized martingale difference divergence: Detecting conditional mean independence with applications in variable screening. Comput Stat Data Anal 2022. [DOI: 10.1016/j.csda.2022.107618] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
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6
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Pan Y. Feature screening and FDR control with knockoff features for ultrahigh-dimensional right-censored data. Comput Stat Data Anal 2022; 173:107504. [DOI: 10.1016/j.csda.2022.107504] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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7
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Honda T, Lin C. Forward variable selection for ultra-high dimensional quantile regression models. ANN I STAT MATH. [DOI: 10.1007/s10463-022-00849-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/01/2022]
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8
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Song F, Lai P, Shen B, Zhu L. Model free feature screening for ultrahigh dimensional covariates with right censored outcomes. COMMUN STAT-SIMUL C 2022. [DOI: 10.1080/03610918.2020.1775848] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- Fengli Song
- School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, China
| | - Peng Lai
- School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, China
| | - Baohua Shen
- School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, China
| | - Lianhua Zhu
- School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, China
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9
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Qu L, Wang X, Sun L. Variable screening for varying coefficient models with ultrahigh-dimensional survival data. Comput Stat Data Anal 2022. [DOI: 10.1016/j.csda.2022.107498] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
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10
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Tong Z, Cai Z, Yang S, Li R. Model-Free Conditional Feature Screening with FDR Control. J Am Stat Assoc 2022. [DOI: 10.1080/01621459.2022.2063130] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- Zhaoxue Tong
- Pennsylvania State University, University Park, PA
| | | | | | - Runze Li
- Pennsylvania State University, University Park, PA
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11
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Liu J, Si Y, Niu Y, Zhang R. Projection quantile correlation and its use in high-dimensional grouped variable screening. Comput Stat Data Anal 2022. [DOI: 10.1016/j.csda.2021.107369] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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12
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Affiliation(s)
- Mingyue Du
- Department of Applied Mathematics The Hong Kong Polytechnic University Hong Kong China
| | - Jianguo Sun
- Department of Statistics University of Missouri Columbia MO 65211 USA
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13
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Zhang J, Zhou H, Liu Y, Cai J. Conditional screening for ultrahigh-dimensional survival data in case-cohort studies. Lifetime Data Anal 2021; 27:632-661. [PMID: 34417679 PMCID: PMC8561435 DOI: 10.1007/s10985-021-09531-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/23/2020] [Accepted: 08/05/2021] [Indexed: 06/13/2023]
Abstract
The case-cohort design has been widely used to reduce the cost of covariate measurements in large cohort studies. In many such studies, the number of covariates is very large, and the goal of the research is to identify active covariates which have great influence on response. Since the introduction of sure independence screening, screening procedures have achieved great success in terms of effectively reducing the dimensionality and identifying active covariates. However, commonly used screening methods are based on marginal correlation or its variants, they may fail to identify hidden active variables which are jointly important but are weakly correlated with the response. Moreover, these screening methods are mainly proposed for data under the simple random sampling and can not be directly applied to case-cohort data. In this paper, we consider the ultrahigh-dimensional survival data under the case-cohort design, and propose a conditional screening method by incorporating some important prior known information of active variables. This method can effectively detect hidden active variables. Furthermore, it possesses the sure screening property under some mild regularity conditions and does not require any complicated numerical optimization. We evaluate the finite sample performance of the proposed method via extensive simulation studies and further illustrate the new approach through a real data set from patients with breast cancer.
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Affiliation(s)
- Jing Zhang
- School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan, 430073, China
| | - Haibo Zhou
- Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, NC, 27599-7420, USA
| | - Yanyan Liu
- School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China
| | - Jianwen Cai
- Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, NC, 27599-7420, USA.
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14
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Guo C, Lv J, Wu J. Composite quantile regression for ultra-high dimensional semiparametric model averaging. Comput Stat Data Anal 2021. [DOI: 10.1016/j.csda.2021.107231] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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15
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Zhang J, Liu Y. Model-free slice screening for ultrahigh-dimensional survival data. J Appl Stat 2021; 48:1755-1774. [DOI: 10.1080/02664763.2020.1772734] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Jing Zhang
- School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan, Hubei, People's Republic of China
| | - Yanyan Liu
- School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei, People's Republic of China
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17
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Conde‐Amboage M, Van Keilegom I, González‐Manteiga W. A new lack‐of‐fit test for quantile regression with censored data. Scand Stat Theory Appl 2021. [DOI: 10.1111/sjos.12512] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
Affiliation(s)
- Mercedes Conde‐Amboage
- Models of Optimization, Decision, Statistics and Applications Research Group (MODESTYA), Department of Statistics, Mathematical Analysis and Optimization Universidade de Santiago de Compostela Santiago de Compostela Spain
- Research Centre for Operations Research and Statistics (ORSTAT) KU Leuven Leuven Belgium
| | - Ingrid Van Keilegom
- Research Centre for Operations Research and Statistics (ORSTAT) KU Leuven Leuven Belgium
| | - Wenceslao González‐Manteiga
- Models of Optimization, Decision, Statistics and Applications Research Group (MODESTYA), Department of Statistics, Mathematical Analysis and Optimization Universidade de Santiago de Compostela Santiago de Compostela Spain
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18
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Zhang J, Zhou H, Liu Y, Cai J. Feature screening for case‐cohort studies with failure time outcome. Scand Stat Theory Appl 2020; 48:349-370. [DOI: 10.1111/sjos.12503] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Jing Zhang
- School of Statistics and Mathematics Zhongnan University of Economics and Law Wuhan China
| | - Haibo Zhou
- Department of Biostatistics University of North Carolina at Chapel Hill Chapel Hill North Carolina USA
| | - Yanyan Liu
- School of Mathematics and Statistics Wuhan University Wuhan China
| | - Jianwen Cai
- Department of Biostatistics University of North Carolina at Chapel Hill Chapel Hill North Carolina USA
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19
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Hu Q, Zhu L, Liu Y, Sun J, Srivastava DK, Robison LL. Nonparametric screening and feature selection for ultrahigh-dimensional Case II interval-censored failure time data. Biom J 2020; 62:1909-1925. [PMID: 32677168 PMCID: PMC7988961 DOI: 10.1002/bimj.201900154] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2019] [Revised: 05/16/2020] [Accepted: 05/18/2020] [Indexed: 11/07/2022]
Abstract
For the analysis of ultrahigh-dimensional data, the first step is often to perform screening and feature selection to effectively reduce the dimensionality while retaining all the active or relevant variables with high probability. For this, many methods have been developed under various frameworks but most of them only apply to complete data. In this paper, we consider an incomplete data situation, case II interval-censored failure time data, for which there seems to be no screening procedure. Basing on the idea of cumulative residual, a model-free or nonparametric method is developed and shown to have the sure independent screening property. In particular, the approach is shown to tend to rank the active variables above the inactive ones in terms of their association with the failure time of interest. A simulation study is conducted to demonstrate the usefulness of the proposed method and, in particular, indicates that it works well with general survival models and is capable of capturing the nonlinear covariates with interactions. Also the approach is applied to a childhood cancer survivor study that motivated this investigation.
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Affiliation(s)
- Qiang Hu
- School of Statistics, Renmin University of China, Beijing, P. R. China
| | - Liang Zhu
- Division of Clinical and Translational Sciences, Department of Internal Medicine, University of Texas Health Science Center at Houston, Houston, TX, USA
| | - Yanyan Liu
- School of Mathematics and Statistics, Wuhan University, Wuhan, P. R. China
| | - Jianguo Sun
- Department of Statistics, University of Missouri, Columbia, MO, USA
| | - Deo Kumar Srivastava
- Biostatistics Department, St. Jude Children’s Research Hospital, Memphis, TN, USA
| | - Leslie L. Robison
- Epidemiology and Cancer Control, St. Jude Children’s Research Hospital, Memphis, TN, USA
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20
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Affiliation(s)
- Jinfeng Xu
- Department of Statistics Actuarial Science The University of Hong Kong Hong Kong
| | - Wai Keung Li
- Faculty of Liberal Arts and Social Sciences The Education University of Hong Kong Hong Kong
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21
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22
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Chen X, Liu CC, Xu S. An efficient algorithm for joint feature screening in ultrahigh-dimensional Cox’s model. Comput Stat 2021; 36:885-910. [DOI: 10.1007/s00180-020-01032-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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23
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Affiliation(s)
- Wanjun Liu
- Department of Statistics, The Pennsylvania State University, University Park, PA
| | - Yuan Ke
- Department of Statistics, University of Georgia, Athens, GA
| | - Jingyuan Liu
- MOE Key Laboratory of Econometrics, Department of Statistics, School of Economics, Wang Yanan Institute for Studies in Economics, and Fujian Key Lab of Statistics, Xiamen University, Xiamen, China
| | - Runze Li
- Department of Statistics, The Pennsylvania State University, University Park, PA
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24
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Chen X, Liu W, Chen X. Model-free survival conditional feature screening. COMMUN STAT-SIMUL C 2020. [DOI: 10.1080/03610918.2020.1779293] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- Xiaolin Chen
- School of Statistics, Qufu Normal University, Qufu, China
| | - Wei Liu
- School of Statistics, Qufu Normal University, Qufu, China
| | - Xiaojing Chen
- School of Statistics, Qufu Normal University, Qufu, China
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25
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Liu Z, Xiong Z. Non-marginal feature screening for additive hazard model with ultrahigh-dimensional covariates. COMMUN STAT-THEOR M 2020. [DOI: 10.1080/03610926.2020.1770288] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Zili Liu
- School of Mathematics and Statistics, Central China Normal University, Wuhan, China
| | - Zikang Xiong
- School of Mathematics and Statistics, Central China Normal University, Wuhan, China
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26
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Affiliation(s)
- Yi Liu
- School of Mathematical Sciences, Ocean University of China, Qingdao, China
| | - Xiaolin Chen
- School of Statistics, Qufu Normal University, Qufu, China
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27
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28
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Song F, Lai P, Shen B. Robust composite weighted quantile screening for ultrahigh dimensional discriminant analysis. METRIKA 2020; 83:799-820. [DOI: 10.1007/s00184-019-00758-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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29
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30
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Affiliation(s)
- Peng Lai
- School of Mathematics and Statistics, Nanjing University of Information Science & Technology, Nanjing, People's Republic of China
| | - Yuanxing Chen
- Department of Statistics, School of Economics, Xiamen University, Xiamen, People's Republic of China
| | - Jie Zhang
- School of Mathematics and Statistics, Nanjing University of Information Science & Technology, Nanjing, People's Republic of China
| | - Bingying Dai
- Department of Statistics, School of Economics, Xiamen University, Xiamen, People's Republic of China
| | - Qingzhao Zhang
- Department of Statistics, School of Economics, Xiamen University, Xiamen, People's Republic of China
- Key Laboratory of Econometrics, Ministry of Education, Xiamen University, Xiamen, People's Republic of China
- Wang Yanan Institute for Studies in Economics, Xiamen University, Xiamen, People's Republic of China
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31
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Yan A, Song F. Adaptive elastic net-penalized quantile regression for variable selection. COMMUN STAT-THEOR M 2019. [DOI: 10.1080/03610926.2018.1508711] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Ailing Yan
- Institute of Mathematics, Hebei University of Technology, Tianjin, China
| | - Fengli Song
- School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, China
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32
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Kong Y, Li Y, Zerom D. Screening and selection for quantile regression using an alternative measure of variable importance. J MULTIVARIATE ANAL 2019; 173:435-55. [DOI: 10.1016/j.jmva.2019.04.007] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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33
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Fang J. Feature screening for ultrahigh-dimensional survival data when failure indicators are missing at random. Stat Pap (Berl) 2021; 62:1141-66. [DOI: 10.1007/s00362-019-01128-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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34
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35
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Affiliation(s)
- Jing Pan
- School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai, China
| | - Shucong Zhang
- School of Mathematical Sciences and Center for Statistical Science, Peking University, Beijing, China
| | - Yong Zhou
- Key Laboratory of Advanced Theory and Application in Statistics and Data Science, MOE, and Institute of Statistics and Interdisciplinary Sciences and School of Statistics, East China Normal University, Shanghai, China
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36
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Zhu L, Zhang Y, Xu K. Measuring and testing for interval quantile dependence. Ann Stat 2018. [DOI: 10.1214/17-aos1635] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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37
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Li X, Ma X, Zhang J. Conditional quantile correlation screening procedure for ultrahigh-dimensional varying coefficient models. J Stat Plan Inference 2018. [DOI: 10.1016/j.jspi.2017.12.005] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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38
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Affiliation(s)
- Meiling Hao
- School of Statistics, University of International Business and Economics, Beijing, People's Republic of China
| | - Yuanyuan Lin
- Department of Statistics, The Chinese University of Hong Kong, Shatin, Hong Kong, People's Republic of China
| | - Xianhui Liu
- School of Statistics and Research Center of Applied Statistics, Jiangxi University of Finance and Economics, Nanchang, People's Republic of China
| | - Wenlu Tang
- Department of Statistics, The Chinese University of Hong Kong, Shatin, Hong Kong, People's Republic of China
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39
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Chen X, Liu Y, Wang Q. Joint feature screening for ultra-high-dimensional sparse additive hazards model by the sparsity-restricted pseudo-score estimator. ANN I STAT MATH 2019; 71:1007-31. [DOI: 10.1007/s10463-018-0675-8] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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40
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41
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Pan J, Yu Y, Zhou Y. Nonparametric independence feature screening for ultrahigh-dimensional survival data. METRIKA 2018; 81:821-47. [DOI: 10.1007/s00184-018-0660-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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42
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Affiliation(s)
- Xiaolin Chen
- School of Statistics, Qufu Normal University, Qufu, People's Republic of China
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Zhang J, Yin G, Liu Y, Wu Y. Censored cumulative residual independent screening for ultrahigh-dimensional survival data. Lifetime Data Anal 2018; 24:273-292. [PMID: 28550654 DOI: 10.1007/s10985-017-9395-2] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/03/2015] [Accepted: 05/16/2017] [Indexed: 05/12/2023]
Abstract
For complete ultrahigh-dimensional data, sure independent screening methods can effectively reduce the dimensionality while retaining all the active variables with high probability. However, limited screening methods have been developed for ultrahigh-dimensional survival data subject to censoring. We propose a censored cumulative residual independent screening method that is model-free and enjoys the sure independent screening property. Active variables tend to be ranked above the inactive ones in terms of their association with the survival times. Compared with several existing methods, our model-free screening method works well with general survival models, and it is invariant to the monotone transformation of the responses, as well as requiring substantially weaker moment conditions. Numerical studies demonstrate the usefulness of the censored cumulative residual independent screening method, and the new approach is illustrated with a gene expression data set.
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Affiliation(s)
- Jing Zhang
- School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, Hubei, China
| | - Guosheng Yin
- Department of Statistics and Actuarial Science, University of Hong Kong, Pokfulam Road, Hong Kong, China
| | - Yanyan Liu
- School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, Hubei, China
| | - Yuanshan Wu
- School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, Hubei, China.
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45
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46
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Affiliation(s)
- Yi Liu
- College of Science, China University of Petroleum (East China), Qingdao, People's Republic of China
| | - Xiaolin Chen
- School of Statistics, Qufu Normal University, Qufu, People's Republic of China
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47
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Affiliation(s)
- Min Chen
- School of Management, University of Science and Technology of China, Hefei City, People's Republic of China
- AMSS, The Chinese Academy of Sciences, Beijing, People's Republic of China
| | - Yimin Lian
- School of Management, University of Science and Technology of China, Hefei City, People's Republic of China
| | - Zhao Chen
- Department of Statistics, Pennsylvania State University, State College, PA, USA
| | - Zhengjun Zhang
- Department of Statistics, University of Wisconsin, Madison, WI, USA
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48
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49
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Abstract
In quantile linear regression with ultra-high dimensional data, we propose an algorithm for screening all candidate variables and subsequently selecting relevant predictors. Specifically, we first employ quantile partial correlation for screening, and then we apply the extended Bayesian information criterion (EBIC) for best subset selection. Our proposed method can successfully select predictors when the variables are highly correlated, and it can also identify variables that make a contribution to the conditional quantiles but are marginally uncorrelated or weakly correlated with the response. Theoretical results show that the proposed algorithm can yield the sure screening set. By controlling the false selection rate, model selection consistency can be achieved theoretically. In practice, we proposed using EBIC for best subset selection so that the resulting model is screening consistent. Simulation studies demonstrate that the proposed algorithm performs well, and an empirical example is presented.
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Affiliation(s)
- Shujie Ma
- Assistant Professor, Department of Statistics, University of California-Riverside, Riverside, CA 92521
| | - Runze Li
- Verne M. Willaman Professor, Department of Statistics, the Pennsylvania State University, University Park, PA 16802
| | - Chih-Ling Tsai
- Distinguished Professor and Robert W. Glock Endowed Chair in Management, Graduate School of Management, University of California at Davis, Davis, CA 95616
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