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Varying Coefficient Regression Models: A Review and New Developments

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  • Byeong U. Park
  • Enno Mammen
  • Young K. Lee
  • Eun Ryung Lee

Abstract

type="main" xml:id="insr12029-abs-0001"> Varying coefficient regression models are known to be very useful tools for analysing the relation between a response and a group of covariates. Their structure and interpretability are similar to those for the traditional linear regression model, but they are more flexible because of the infinite dimensionality of the corresponding parameter spaces. The aims of this paper are to give an overview on the existing methodological and theoretical developments for varying coefficient models and to discuss their extensions with some new developments. The new developments enable us to use different amount of smoothing for estimating different component functions in the models. They are for a flexible form of varying coefficient models that requires smoothing across different covariates' spaces and are based on the smooth backfitting technique that is admitted as a powerful technique for fitting structural regression models and is also known to free us from the curse of dimensionality.

Suggested Citation

  • Byeong U. Park & Enno Mammen & Young K. Lee & Eun Ryung Lee, 2015. "Varying Coefficient Regression Models: A Review and New Developments," International Statistical Review, International Statistical Institute, vol. 83(1), pages 36-64, April.
    • Handle: RePEc:bla:istatr:v:83:y:2015:i:1:p:36-64
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    3. Samuele CENTORRINO & Jeffrey S. RACINE, 2017. "Semiparametric Varying Coefficient Models with Endogenous Covariates," Annals of Economics and Statistics, GENES, issue 128, pages 261-295.
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    5. Yongsheng Jiang & Dong Zhao & Andrew Sanderford & Jing Du, 2018. "Effects of Bank Lending on Urban Housing Prices for Sustainable Development: A Panel Analysis of Chinese Cities," Sustainability, MDPI, vol. 10(3), pages 1-16, February.
    6. Zhang, Xiaoke & Zhong, Qixian & Wang, Jane-Ling, 2020. "A new approach to varying-coefficient additive models with longitudinal covariates," Computational Statistics & Data Analysis, Elsevier, vol. 145(C).
    7. Christoph Breunig, 2018. "Varying Random Coefficient Models," Papers 1804.03110, arXiv.org, revised Aug 2020.
    8. Djeundje, Viani Biatat & Crook, Jonathan, 2019. "Dynamic survival models with varying coefficients for credit risks," European Journal of Operational Research, Elsevier, vol. 275(1), pages 319-333.
    9. Olarreaga, Marcelo & Sperlich, Stefan & Trachsel, Virginie, 2016. "Export Promotion: what works?," CEPR Discussion Papers 11270, C.E.P.R. Discussion Papers.
    10. Chen, Jia & Li, Degui & Xia, Yingcun, 2019. "Estimation of a rank-reduced functional-coefficient panel data model with serial correlation," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 456-479.
    11. Koo, Chao, 2018. "Essays on functional coefficient models," Other publications TiSEM ba87b8a5-3c55-40ec-967d-9, Tilburg University, School of Economics and Management.
    12. Lee, Kyeongeun & Lee, Young K. & Park, Byeong U. & Yang, Seong J., 2018. "Time-dynamic varying coefficient models for longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 123(C), pages 50-65.
    13. Loann David Denis Desboulets, 2018. "A Review on Variable Selection in Regression Analysis," Econometrics, MDPI, vol. 6(4), pages 1-27, November.
    14. Sunil Kanwar & Stefan Sperlich, 2023. "Direct foreign investment and intellectual property reform in the South," Journal of International Development, John Wiley & Sons, Ltd., vol. 35(6), pages 1456-1477, August.
    15. Breunig, Christoph, 2021. "Varying random coefficient models," Journal of Econometrics, Elsevier, vol. 221(2), pages 381-408.
    16. Jooyong Shim & Changha Hwang & Kyungha Seok, 2016. "Support vector quantile regression with varying coefficients," Computational Statistics, Springer, vol. 31(3), pages 1015-1030, September.
    17. Han, Kyunghee & Lee, Young K. & Park, Byeong U., 2020. "Smooth backfitting for errors-in-variables varying coefficient regression models," Computational Statistics & Data Analysis, Elsevier, vol. 145(C).
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    19. Ingrid Mauerer & Gerhard Tutz, 2023. "Heterogeneity in general multinomial choice models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(1), pages 129-148, March.

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