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Shrinkage estimation of the varying-coefficient model with continuous and categorical covariates

Author

Listed:
  • Han, Xiaoyi
  • Peng, Bin
  • Yang, Yanrong
  • Zhu, Huanjun

Abstract

This paper studies shrinkage estimation of a general varying-coefficient model in Li and Racine (2010), with both continuous and categorical covariates. We propose a kernel least absolute shrinkage and selection operator (KLASSO) to implement estimation and variable selection for the model. We establish the estimation sparsity and oracle efficiency of the KLASSO estimator. We also provide a BIC-type criterion for tuning parameter selection and justify the model selection consistency. Simulation results suggest our method has a nice performance in terms of estimation errors and variable selection.

Suggested Citation

  • Han, Xiaoyi & Peng, Bin & Yang, Yanrong & Zhu, Huanjun, 2021. "Shrinkage estimation of the varying-coefficient model with continuous and categorical covariates," Economics Letters, Elsevier, vol. 202(C).
    • Handle: RePEc:eee:ecolet:v:202:y:2021:i:c:s0165176521000963
    DOI: 10.1016/j.econlet.2021.109819
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    References listed on IDEAS

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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. Jianqing Fan & Yunbei Ma & Wei Dai, 2014. "Nonparametric Independence Screening in Sparse Ultra-High-Dimensional Varying Coefficient Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1270-1284, September.
    3. Zhang, Qi & Wang, Youfa, 2004. "Socioeconomic inequality of obesity in the United States: do gender, age, and ethnicity matter?," Social Science & Medicine, Elsevier, vol. 58(6), pages 1171-1180, March.
    4. Li, Qi & Racine, Jeffrey S., 2010. "Smooth Varying-Coefficient Estimation And Inference For Qualitative And Quantitative Data," Econometric Theory, Cambridge University Press, vol. 26(6), pages 1607-1637, December.
    5. 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.
    6. 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.
    7. 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.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Variable selection; Varying-coefficient model; Least absolute shrinkage and selection operator; Asymptotic theory;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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