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Gradient-based smoothing parameter selection for nonparametric regression estimation

Author

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  • Henderson, Daniel J.
  • Li, Qi
  • Parmeter, Christopher F.
  • Yao, Shuang

Abstract

Estimating gradients is of crucial importance across a broad range of applied economic domains. Here we consider data-driven bandwidth selection based on the gradient of an unknown regression function. This is a difficult problem given that direct observation of the value of the gradient is typically not observed. The procedure developed here delivers bandwidths which behave asymptotically as though they were selected knowing the true gradient. Simulated examples showcase the finite sample attraction of this new mechanism and confirm the theoretical predictions.

Suggested Citation

  • Henderson, Daniel J. & Li, Qi & Parmeter, Christopher F. & Yao, Shuang, 2015. "Gradient-based smoothing parameter selection for nonparametric regression estimation," Journal of Econometrics, Elsevier, vol. 184(2), pages 233-241.
    • Handle: RePEc:eee:econom:v:184:y:2015:i:2:p:233-241
    DOI: 10.1016/j.jeconom.2014.09.007
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    Cited by:

    1. Lin, Wei & Cai, Zongwu & Li, Zheng & Su, Li, 2015. "Optimal smoothing in nonparametric conditional quantile derivative function estimation," Journal of Econometrics, Elsevier, vol. 188(2), pages 502-513.
    2. Shakeeb Khan & Arnaud Maurel & Yichong Zhang, 2023. "Informational Content of Factor Structures in Simultaneous Binary Response Models," Advances in Econometrics, in: Essays in Honor of Joon Y. Park: Econometric Methodology in Empirical Applications, volume 45, pages 385-410, Emerald Group Publishing Limited.
    3. Léopold Simar & Ingrid Keilegom & Valentin Zelenyuk, 2017. "Nonparametric least squares methods for stochastic frontier models," Journal of Productivity Analysis, Springer, vol. 47(3), pages 189-204, June.
    4. Li, Cong & Wang, Yanfei, 2016. "Gradient-based bandwidth selection for estimating average derivatives," Economics Letters, Elsevier, vol. 140(C), pages 19-22.
    5. Zhou, Jianhua & Parmeter, Christopher F. & Kumbhakar, Subal C., 2020. "Nonparametric estimation of the determinants of inefficiency in the presence of firm heterogeneity," European Journal of Operational Research, Elsevier, vol. 286(3), pages 1142-1152.
    6. Salim Bouzebda & Mohamed Chaouch & Sultana Didi Biha, 2022. "Asymptotics for function derivatives estimators based on stationary and ergodic discrete time processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(4), pages 737-771, August.
    7. Xie, Qichang & Sun, Qiankun, 2019. "Computation and application of robust data-driven bandwidth selection for gradient function estimation," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 274-293.
    8. Wei, Jie & Zhang, Yonghui, 2020. "A time-varying diffusion index forecasting model," Economics Letters, Elsevier, vol. 193(C).
    9. Geng, Xin & Sun, Kai, 2019. "Gradient estimation of the local-constant semiparametric smooth coefficient model," Economics Letters, Elsevier, vol. 185(C).
    10. Christopher F. Parmeter & Valentin Zelenyuk, 2016. "A Bridge Too Far? The State of the Art in Combining the Virtues of Stochastic Frontier Analysis and Data Envelopement Analysis," Working Papers 2016-10, University of Miami, Department of Economics.

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    More about this item

    Keywords

    Gradient estimation; Kernel smoothing; Least squares cross validation;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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