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A More Accurate Estimation of Semiparametric Logistic Regression

Author

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  • Xia Zheng

    (Faculty of Science, College of Statistics and Data Science, Beijing University of Technology, Beijing 100124, China
    These authors contributed equally to this work.)

  • Yaohua Rong

    (Faculty of Science, College of Statistics and Data Science, Beijing University of Technology, Beijing 100124, China
    These authors contributed equally to this work.)

  • Ling Liu

    (Faculty of Science, College of Statistics and Data Science, Beijing University of Technology, Beijing 100124, China)

  • Weihu Cheng

    (Faculty of Science, College of Statistics and Data Science, Beijing University of Technology, Beijing 100124, China)

Abstract

Growing interest in genomics research has called for new semiparametric models based on kernel machine regression for modeling health outcomes. Models containing redundant predictors often show unsatisfactory prediction performance. Thus, our task is to construct a method which can guarantee the estimation accuracy by removing redundant variables. Specifically, in this paper, based on the regularization method and an innovative class of garrotized kernel functions, we propose a novel penalized kernel machine method for a semiparametric logistic model. Our method can promise us high prediction accuracies, due to its capability of flexibly describing the complicated relationship between responses and predictors and its compatibility of the interactions among the predictors. In addition, our method can also remove the redundant variables. Our numerical experiments demonstrate that our method yields higher prediction accuracies compared to competing approaches.

Suggested Citation

  • Xia Zheng & Yaohua Rong & Ling Liu & Weihu Cheng, 2021. "A More Accurate Estimation of Semiparametric Logistic Regression," Mathematics, MDPI, vol. 9(19), pages 1-12, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:19:p:2376-:d:642629
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    1. Hai-Hui Huang & Xiao-Ying Liu & Yong Liang, 2016. "Feature Selection and Cancer Classification via Sparse Logistic Regression with the Hybrid L1/2 +2 Regularization," PLOS ONE, Public Library of Science, vol. 11(5), pages 1-15, May.
    2. Zakariya Yahya Algamal & Muhammad Hisyam Lee, 2019. "A two-stage sparse logistic regression for optimal gene selection in high-dimensional microarray data classification," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(3), pages 753-771, September.
    3. Dawei Liu & Xihong Lin & Debashis Ghosh, 2007. "Semiparametric Regression of Multidimensional Genetic Pathway Data: Least-Squares Kernel Machines and Linear Mixed Models," Biometrics, The International Biometric Society, vol. 63(4), pages 1079-1088, December.
    4. 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.
    5. Arnab Maity & Xihong Lin, 2011. "Powerful Tests for Detecting a Gene Effect in the Presence of Possible Gene–Gene Interactions Using Garrote Kernel Machines," Biometrics, The International Biometric Society, vol. 67(4), pages 1271-1284, December.
    6. 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.
    7. Friedman, Jerome H. & Hastie, Trevor & Tibshirani, Rob, 2010. "Regularization Paths for Generalized Linear Models via Coordinate Descent," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i01).
    8. 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.
    9. Lee, Sangin & Kwon, Sunghoon & Kim, Yongdai, 2016. "A modified local quadratic approximation algorithm for penalized optimization problems," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 275-286.
    10. Jing Qian & Seyedmehdi Payabvash & André Kemmling & Michael H. Lev & Lee H. Schwamm & Rebecca A. Betensky, 2014. "Variable selection and prediction using a nested, matched case-control study: Application to hospital acquired pneumonia in stroke patients," Biometrics, The International Biometric Society, vol. 70(1), pages 153-163, March.
    11. Gaorong Li & Liugen Xue & Heng Lian, 2012. "SCAD-penalised generalised additive models with non-polynomial dimensionality," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(3), pages 681-697.
    12. Pradeep Ravikumar & John Lafferty & Han Liu & Larry Wasserman, 2009. "Sparse additive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(5), pages 1009-1030, November.
    13. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    14. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
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    Cited by:

    1. Rong Liu & Shishun Zhao & Tao Hu & Jianguo Sun, 2022. "Variable Selection for Generalized Linear Models with Interval-Censored Failure Time Data," Mathematics, MDPI, vol. 10(5), pages 1-18, February.

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