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Sure independence screening in the presence of missing data

Author

Listed:
  • Adriano Zanin Zambom

    (California State University, Northridge)

  • Gregory J. Matthews

    (Loyola University Chicago)

Abstract

Variable selection in ultra-high dimensional data sets is an increasingly prevalent issue with the readily available data arising from, for example, genome-wide associations studies or gene expression data. When the dimension of the feature space is exponentially larger than the sample size, it is desirable to screen out unimportant predictors in order to bring the dimension down to a moderate scale. In this paper we consider the case when observations of the predictors are missing at random. We propose performing screening using the marginal linear correlation coefficient between each predictor and the response variable accounting for the missing data using maximum likelihood estimation. This method is shown to have the sure screening property. Moreover, a novel method of screening that uses additional predictors when estimating the correlation coefficient is proposed. Simulations show that simply performing screening using pairwise complete observations is out-performed by both the proposed methods and is not recommended. Finally, the proposed methods are applied to a gene expression study on prostate cancer.

Suggested Citation

  • Adriano Zanin Zambom & Gregory J. Matthews, 2021. "Sure independence screening in the presence of missing data," Statistical Papers, Springer, vol. 62(2), pages 817-845, April.
    • Handle: RePEc:spr:stpapr:v:62:y:2021:i:2:d:10.1007_s00362-019-01115-w
    DOI: 10.1007/s00362-019-01115-w
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    References listed on IDEAS

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    1. Jingyuan Liu & Runze Li & Rongling Wu, 2014. "Feature Selection for Varying Coefficient Models With Ultrahigh-Dimensional Covariates," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 266-274, March.
    2. Horton, Nicholas J. & Kleinman, Ken P., 2007. "Much Ado About Nothing: A Comparison of Missing Data Methods and Software to Fit Incomplete Data Regression Models," The American Statistician, American Statistical Association, vol. 61, pages 79-90, February.
    3. Lansangan, Joseph Ryan G. & Barrios, Erniel B., 2017. "Simultaneous dimension reduction and variable selection in modeling high dimensional data," Computational Statistics & Data Analysis, Elsevier, vol. 112(C), pages 242-256.
    4. Chung-Wei Shen & Yi-Hau Chen, 2012. "Model Selection for Generalized Estimating Equations Accommodating Dropout Missingness," Biometrics, The International Biometric Society, vol. 68(4), pages 1046-1054, December.
    5. Ibrahim, Joseph G. & Zhu, Hongtu & Tang, Niansheng, 2008. "Model Selection Criteria for Missing-Data Problems Using the EM Algorithm," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1648-1658.
    6. Hu Yang & Huilan Liu, 2016. "Penalized weighted composite quantile estimators with missing covariates," Statistical Papers, Springer, vol. 57(1), pages 69-88, March.
    7. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    8. Jiang, Xuejun & Li, Jingzhi & Xia, Tian & Yan, Wanfeng, 2016. "Robust and efficient estimation with weighted composite quantile regression," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 457(C), pages 413-423.
    9. Hu Yang & Chaohui Guo & Jing Lv, 2016. "Variable selection for generalized varying coefficient models with longitudinal data," Statistical Papers, Springer, vol. 57(1), pages 115-132, March.
    10. Joel L. Horowitz, 2015. "Variable selection and estimation in high-dimensional models," Canadian Journal of Economics, Canadian Economics Association, vol. 48(2), pages 389-407, May.
    11. Scott A. Tomlins & Bharathi Laxman & Saravana M. Dhanasekaran & Beth E. Helgeson & Xuhong Cao & David S. Morris & Anjana Menon & Xiaojun Jing & Qi Cao & Bo Han & Jindan Yu & Lei Wang & James E. Montie, 2007. "Distinct classes of chromosomal rearrangements create oncogenic ETS gene fusions in prostate cancer," Nature, Nature, vol. 448(7153), pages 595-599, August.
    12. Joel L. Horowitz, 2015. "Variable selection and estimation in high-dimensional models," CeMMAP working papers CWP35/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    13. Mohammed Attouch & Ali Laksaci & Nafissa Messabihi, 2017. "Nonparametric relative error regression for spatial random variables," Statistical Papers, Springer, vol. 58(4), pages 987-1008, December.
    14. N. Neykov & P. Filzmoser & P. Neytchev, 2014. "Erratum to: Ultrahigh dimensional variable selection through the penalized maximum trimmed likelihood estimator," Statistical Papers, Springer, vol. 55(3), pages 917-918, August.
    15. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    16. Qihua Wang & Yongjin Li, 2018. "How to Make Model†free Feature Screening Approaches for Full Data Applicable to the Case of Missing Response?," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 45(2), pages 324-346, June.
    17. Fan, Jianqing & Feng, Yang & Song, Rui, 2011. "Nonparametric Independence Screening in Sparse Ultra-High-Dimensional Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 544-557.
    18. Xiaowei Yang & Thomas R. Belin & W. John Boscardin, 2005. "Imputation and Variable Selection in Linear Regression Models with Missing Covariates," Biometrics, The International Biometric Society, vol. 61(2), pages 498-506, June.
    19. Joel L. Horowitz, 2015. "Variable selection and estimation in high‐dimensional models," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 48(2), pages 389-407, May.
    20. Rita Faria & Manuel Gomes & David Epstein & Ian White, 2014. "A Guide to Handling Missing Data in Cost-Effectiveness Analysis Conducted Within Randomised Controlled Trials," PharmacoEconomics, Springer, vol. 32(12), pages 1157-1170, December.
    21. N. Neykov & P. Filzmoser & P. Neytchev, 2014. "Ultrahigh dimensional variable selection through the penalized maximum trimmed likelihood estimator," Statistical Papers, Springer, vol. 55(1), pages 187-207, February.
    22. Gerda Claeskens & Fabrizio Consentino, 2008. "Variable Selection with Incomplete Covariate Data," Biometrics, The International Biometric Society, vol. 64(4), pages 1062-1069, December.
    23. Lai, Peng & Liu, Yiming & Liu, Zhi & Wan, Yi, 2017. "Model free feature screening for ultrahigh dimensional data with responses missing at random," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 201-216.
    24. Karsten Suhre & Matthias Arnold & Aditya Mukund Bhagwat & Richard J. Cotton & Rudolf Engelke & Johannes Raffler & Hina Sarwath & Gaurav Thareja & Annika Wahl & Robert Kirk DeLisle & Larry Gold & Marij, 2017. "Connecting genetic risk to disease end points through the human blood plasma proteome," Nature Communications, Nature, vol. 8(1), pages 1-14, April.
    25. Jianqing Fan & Jinchi Lv, 2008. "Sure independence screening for ultrahigh dimensional feature space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 849-911, November.
    26. Omid Karimi & Mohsen Mohammadzadeh, 2012. "Bayesian spatial regression models with closed skew normal correlated errors and missing observations," Statistical Papers, Springer, vol. 53(1), pages 205-218, February.
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