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Penalized estimation in additive varying coefficient models using grouped regularization

Author

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  • A. Antoniadis
  • I. Gijbels
  • S. Lambert-Lacroix

Abstract

Additive varying coefficient models are a natural extension of multiple linear regression models, allowing the regression coefficients to be functions of other variables. Therefore these models are more flexible to model more complex dependencies in data structures. In this paper we consider the problem of selecting in an automatic way the significant variables among a large set of variables, when the interest is on a given response variable. In recent years several grouped regularization methods have been proposed and in this paper we present these under one unified framework in this varying coefficient model context. For each of the discussed grouped regularization methods we investigate the optimization problem to be solved, possible algorithms for doing so, and the variable and estimation consistency of the methods. We investigate the finite-sample performance of these methods, in a comparative study, and illustrate them on real data examples. Copyright Springer-Verlag Berlin Heidelberg 2014

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  • A. Antoniadis & I. Gijbels & S. Lambert-Lacroix, 2014. "Penalized estimation in additive varying coefficient models using grouped regularization," Statistical Papers, Springer, vol. 55(3), pages 727-750, August.
    • Handle: RePEc:spr:stpapr:v:55:y:2014:i:3:p:727-750
    DOI: 10.1007/s00362-013-0522-1
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    References listed on IDEAS

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    1. Wang, Lifeng & Li, Hongzhe & Huang, Jianhua Z., 2008. "Variable Selection in Nonparametric Varying-Coefficient Models for Analysis of Repeated Measurements," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1556-1569.
    2. Jian Huang & Shuange Ma & Huiliang Xie & Cun-Hui Zhang, 2009. "A group bridge approach for variable selection," Biometrika, Biometrika Trust, vol. 96(2), pages 339-355.
    3. 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.
    4. Wang, Hansheng & Xia, Yingcun, 2009. "Shrinkage Estimation of the Varying Coefficient Model," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 747-757.
    5. J. Fan & J.‐T. Zhang, 2000. "Two‐step estimation of functional linear models with applications to longitudinal data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 303-322.
    6. Lukas Meier & Sara Van De Geer & Peter Bühlmann, 2008. "The group lasso for logistic regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 53-71, February.
    7. Colin Wu & Kai Yu & Chin-Tsang Chiang, 2000. "A Two-Step Smoothing Method for Varying-Coefficient Models with Repeated Measurements," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(3), pages 519-543, September.
    8. Tang Qingguo & Cheng Longsheng, 2012. "Componentwise B-spline estimation for varying coefficient models with longitudinal data," Statistical Papers, Springer, vol. 53(3), pages 629-652, August.
    9. 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.
    10. Harrison, David Jr. & Rubinfeld, Daniel L., 1978. "Hedonic housing prices and the demand for clean air," Journal of Environmental Economics and Management, Elsevier, vol. 5(1), pages 81-102, March.
    11. Jianhua Z. Huang, 2002. "Varying-coefficient models and basis function approximations for the analysis of repeated measurements," Biometrika, Biometrika Trust, vol. 89(1), pages 111-128, March.
    12. Wang, Hansheng & Leng, Chenlei, 2007. "Unified LASSO Estimation by Least Squares Approximation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1039-1048, September.
    13. 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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    Cited by:

    1. 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.
    2. Chaohui Guo & Hu Yang & Jing Lv, 2018. "Two step estimations for a single-index varying-coefficient model with longitudinal data," Statistical Papers, Springer, vol. 59(3), pages 957-983, September.
    3. Ning Li & Hu Yang, 2021. "Nonnegative estimation and variable selection under minimax concave penalty for sparse high-dimensional linear regression models," Statistical Papers, Springer, vol. 62(2), pages 661-680, April.
    4. Wu Cen & Zhong Ping-Shou & Cui Yuehua, 2018. "Additive varying-coefficient model for nonlinear gene-environment interactions," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 17(2), pages 1-18, April.
    5. Zambom, Adriano Zanin & Akritas, Michael G., 2017. "NonpModelCheck: An R Package for Nonparametric Lack-of-Fit Testing and Variable Selection," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 77(i10).
    6. Li Liu & Hao Wang & Yanyan Liu & Jian Huang, 2021. "Model pursuit and variable selection in the additive accelerated failure time model," Statistical Papers, Springer, vol. 62(6), pages 2627-2659, December.
    7. Chaohui Guo & Hu Yang & Jing Lv, 2017. "Robust variable selection in high-dimensional varying coefficient models based on weighted composite quantile regression," Statistical Papers, Springer, vol. 58(4), pages 1009-1033, December.
    8. Caiya Zhang & Yanbiao Xiang, 2016. "On the oracle property of adaptive group Lasso in high-dimensional linear models," Statistical Papers, Springer, vol. 57(1), pages 249-265, March.

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