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Spline-Backfitted Kernel Smoothing Of Additive Coefficient Model

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  • Liu, Rong
  • Yang, Lijian

Abstract

Additive coefficient model (Xue and Yang, 2006a, 2006b) is a flexible regression and autoregression tool that circumvents the “curse of dimensionality.” We propose spline-backfitted kernel (SBK) and spline-backfitted local linear (SBLL) estimators for the component functions in the additive coefficient model that are both (i) computationally expedient so they are usable for analyzing high dimensional data, and (ii) theoretically reliable so inference can be made on the component functions with confidence. In addition, they are (iii) intuitively appealing and easy to use for practitioners. The SBLL procedure is applied to a varying coefficient extension of the Cobb-Douglas model for the U.S. GDP that allows nonneutral effects of the R&D on capital and labor as well as in total factor productivity (TFP).

Suggested Citation

  • Liu, Rong & Yang, Lijian, 2010. "Spline-Backfitted Kernel Smoothing Of Additive Coefficient Model," Econometric Theory, Cambridge University Press, vol. 26(1), pages 29-59, February.
    • Handle: RePEc:cup:etheor:v:26:y:2010:i:01:p:29-59_09
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    Citations

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    Cited by:

    1. Rong Liu & Yichuan Zhao, 2021. "Empirical likelihood inference for generalized additive partially linear models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(3), pages 569-585, September.
    2. Shuzhuan Zheng & Rong Liu & Lijian Yang & Wolfgang K. Härdle, 2016. "Statistical inference for generalized additive models: simultaneous confidence corridors and variable selection," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(4), pages 607-626, December.
    3. Fan, Zengyan & Lian, Heng, 2018. "Quantile regression for additive coefficient models in high dimensions," Journal of Multivariate Analysis, Elsevier, vol. 164(C), pages 54-64.
    4. Xiaoqi Zhang & Yi Chen & Yi Yao, 2021. "Dynamic information asymmetry in micro health insurance: implications for sustainability," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 46(3), pages 468-507, July.
    5. Fengler, M.R. & Mammen, E. & Vogt, M., 2015. "Specification and structural break tests for additive models with applications to realized variance data," Journal of Econometrics, Elsevier, vol. 188(1), pages 196-218.
    6. Lijie Gu & Li Wang & Wolfgang Härdle & Lijian Yang, 2014. "A simultaneous confidence corridor for varying coefficient regression with sparse functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(4), pages 806-843, December.
    7. Tu, Yundong & Wang, Ying, 2022. "Spurious functional-coefficient regression models and robust inference with marginal integration," Journal of Econometrics, Elsevier, vol. 229(2), pages 396-421.
    8. Yoshida, Takuma, 2018. "Semiparametric method for model structure discovery in additive regression models," Econometrics and Statistics, Elsevier, vol. 5(C), pages 124-136.
    9. Shujie Ma & Jeffrey S. Racine & Lijian Yang, 2015. "Spline Regression in the Presence of Categorical Predictors," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(5), pages 705-717, August.
    10. Hongyu An & Boping Tian, 2024. "Varying Index Coefficient Model for Tail Index Regression," Mathematics, MDPI, vol. 12(13), pages 1-34, June.
    11. Patrick, Joshua D. & Harvill, Jane L. & Hansen, Clifford W., 2016. "A semiparametric spatio-temporal model for solar irradiance data," Renewable Energy, Elsevier, vol. 87(P1), pages 15-30.
    12. Hu, Jianhua & You, Jinhong & Zhou, Xian, 2017. "Improved estimation of fixed effects panel data partially linear models with heteroscedastic errors," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 96-111.
    13. Hu, Lixia & Huang, Tao & You, Jinhong, 2019. "Two-step estimation of time-varying additive model for locally stationary time series," Computational Statistics & Data Analysis, Elsevier, vol. 130(C), pages 94-110.
    14. Takuma Yoshida, 2021. "Additive models for extremal quantile regression with Pareto-type distributions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(1), pages 103-134, March.

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