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Homogeneity detection for the high-dimensional generalized linear model

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  • Jeon, Jong-June
  • Kwon, Sunghoon
  • Choi, Hosik

Abstract

We propose to use a penalized estimator for detecting homogeneity of the high-dimensional generalized linear model. Here, the homogeneity is a specific model structure where regression coefficients are grouped having exactly the same value in each group. The proposed estimator achieves weak oracle property under mild regularity conditions and is invariant to the choice of reference levels when there are categorical covariates in the model. An efficient algorithm is also provided. Various numerical studies confirm that the proposed penalized estimator gives better performance than other conventional variable selection estimators when the model has homogeneity.

Suggested Citation

  • Jeon, Jong-June & Kwon, Sunghoon & Choi, Hosik, 2017. "Homogeneity detection for the high-dimensional generalized linear model," Computational Statistics & Data Analysis, Elsevier, vol. 114(C), pages 61-74.
    • Handle: RePEc:eee:csdana:v:114:y:2017:i:c:p:61-74
    DOI: 10.1016/j.csda.2017.04.001
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    1. 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.
    2. Shen, Xiaotong & Huang, Hsin-Cheng, 2010. "Grouping Pursuit Through a Regularization Solution Surface," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 727-739.
    3. Le An & Pham Tao, 2005. "The DC (Difference of Convex Functions) Programming and DCA Revisited with DC Models of Real World Nonconvex Optimization Problems," Annals of Operations Research, Springer, vol. 133(1), pages 23-46, January.
    4. Ye, Gui-Bo & Xie, Xiaohui, 2011. "Split Bregman method for large scale fused Lasso," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1552-1569, April.
    5. Yongdai Kim & Sunghoon Kwon, 2012. "Global optimality of nonconvex penalized estimators," Biometrika, Biometrika Trust, vol. 99(2), pages 315-325.
    6. Yongdai Kim & Jong-June Jeon & Sangmi Han, 2016. "A Necessary Condition for the Strong Oracle Property," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 610-624, June.
    7. Kim, Yongdai & Choi, Hosik & Oh, Hee-Seok, 2008. "Smoothly Clipped Absolute Deviation on High Dimensions," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1665-1673.
    8. Yunzhang Zhu & Xiaotong Shen & Wei Pan, 2013. "Simultaneous Grouping Pursuit and Feature Selection Over an Undirected Graph," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 713-725, June.
    9. 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.
    10. Robert Tibshirani & Michael Saunders & Saharon Rosset & Ji Zhu & Keith Knight, 2005. "Sparsity and smoothness via the fused lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(1), pages 91-108, February.
    11. Howard D. Bondell & Brian J. Reich, 2009. "Simultaneous Factor Selection and Collapsing Levels in ANOVA," Biometrics, The International Biometric Society, vol. 65(1), pages 169-177, March.
    12. Howard D. Bondell & Brian J. Reich, 2008. "Simultaneous Regression Shrinkage, Variable Selection, and Supervised Clustering of Predictors with OSCAR," Biometrics, The International Biometric Society, vol. 64(1), pages 115-123, March.
    13. Xiaotong Shen & Hsin-Cheng Huang & Wei Pan, 2012. "Simultaneous supervised clustering and feature selection over a graph," Biometrika, Biometrika Trust, vol. 99(4), pages 899-914.
    14. Yingying Fan & Cheng Yong Tang, 2013. "Tuning parameter selection in high dimensional penalized likelihood," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(3), pages 531-552, June.
    15. Zheng Tracy Ke & Jianqing Fan & Yichao Wu, 2015. "Homogeneity Pursuit," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 175-194, March.
    16. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
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    1. Zhang, Xiaochen & Zhang, Qingzhao & Ma, Shuangge & Fang, Kuangnan, 2022. "Subgroup analysis for high-dimensional functional regression," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    2. Yang, Xinfeng & Yan, Xiaodong & Huang, Jian, 2019. "High-dimensional integrative analysis with homogeneity and sparsity recovery," Journal of Multivariate Analysis, Elsevier, vol. 174(C).

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