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Gradient Based Smoothing Parameter Selection for Nonparametric Regression Estimation

Author

Listed:
  • Daniel J. Henderson

    (Department of Economics, State University of New York at Binghamton)

  • Qi Li

    (Department of Economics, Texas A&M University)

  • Christopher F. Parmeter

    (Department of Economics, University of Miami)

Abstract

Uncovering gradients is of crucial importance across a broad range of economic environments. Here we consider data-driven bandwidth selection based on the gradient of an unknown regression function. The procedure developed here is automatic and does not require initial estimation of unknown functions with pilot bandwidths. We prove that it delivers bandwidths which have the optimal rate of convergence for the gradient. Both simulated and empirical examples showcase the finite sample attraction of this new mechanism.

Suggested Citation

  • Daniel J. Henderson & Qi Li & Christopher F. Parmeter, 2013. "Gradient Based Smoothing Parameter Selection for Nonparametric Regression Estimation," Working Papers 2014-01, University of Miami, Department of Economics.
    • Handle: RePEc:mia:wpaper:2014-01
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    File URL: https://www.herbert.miami.edu/_assets/files/repec/WP2014-01.pdf
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    References listed on IDEAS

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    1. Pierre-Andre Chiappori & Amit Gandhi & Bernard Salanie & Francois Salanie, 2009. "Identifying Preferences under Risk from Discrete Choices," American Economic Review, American Economic Association, vol. 99(2), pages 356-362, May.
    2. Peter Hall & Qi Li & Jeffrey S. Racine, 2007. "Nonparametric Estimation of Regression Functions in the Presence of Irrelevant Regressors," The Review of Economics and Statistics, MIT Press, vol. 89(4), pages 784-789, November.
    3. Racine, Jeff & Li, Qi, 2004. "Nonparametric estimation of regression functions with both categorical and continuous data," Journal of Econometrics, Elsevier, vol. 119(1), pages 99-130, March.
    4. Anglin, Paul M & Gencay, Ramazan, 1996. "Semiparametric Estimation of a Hedonic Price Function," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(6), pages 633-648, Nov.-Dec..
    5. Patrick Bajari & Matthew E. Kahn, 2005. "Estimating Housing Demand With an Application to Explaining Racial Segregation in Cities," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 20-33, January.
    6. Alicia H. Munnell, 1990. "How does public infrastructure affect regional economic performance?," Conference Series ; [Proceedings], Federal Reserve Bank of Boston, vol. 34, pages 69-112.
    7. Masry, Elias, 1996. "Multivariate regression estimation local polynomial fitting for time series," Stochastic Processes and their Applications, Elsevier, vol. 65(1), pages 81-101, December.
    8. James J. Heckman & Rosa L. Matzkin & Lars Nesheim, 2010. "Nonparametric Identification and Estimation of Nonadditive Hedonic Models," Econometrica, Econometric Society, vol. 78(5), pages 1569-1591, September.
    9. Daniel J. Henderson & Christopher F. Parmeter & Subal C. Kumbhakar, 2007. "Nonparametric estimation of a hedonic price function," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(3), pages 695-699.
    10. Rice, John A., 1986. "Bandwidth choice for differentiation," Journal of Multivariate Analysis, Elsevier, vol. 19(2), pages 251-264, August.
    11. Cai, Zongwu & Fan, Jianqing & Yao, Qiwei, 2000. "Functional-coefficient regression models for nonlinear time series," LSE Research Online Documents on Economics 6314, London School of Economics and Political Science, LSE Library.
    12. Baltagi, Badi H & Pinnoi, Nat, 1995. "Public Capital Stock and State Productivity Growth: Further Evidence from an Error Components Model," Empirical Economics, Springer, vol. 20(2), pages 351-359.
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    Citations

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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. Geng, Xin & Sun, Kai, 2019. "Gradient estimation of the local-constant semiparametric smooth coefficient model," Economics Letters, Elsevier, vol. 185(C).
    4. 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.
    5. Li, Cong & Wang, Yanfei, 2016. "Gradient-based bandwidth selection for estimating average derivatives," Economics Letters, Elsevier, vol. 140(C), pages 19-22.
    6. 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.
    7. 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.
    8. Centorrino, Samuele & Parmeter, Christopher F., 2024. "Nonparametric estimation of stochastic frontier models with weak separability," Journal of Econometrics, Elsevier, vol. 238(2).
    9. 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.
    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.
    11. De Monte Enrico, 2024. "Nonparametric Instrumental Regression with Two-Way Fixed Effects," Journal of Econometric Methods, De Gruyter, vol. 13(1), pages 49-66, January.
    12. Wei, Jie & Zhang, Yonghui, 2020. "A time-varying diffusion index forecasting model," Economics Letters, Elsevier, vol. 193(C).

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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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    This paper has been announced in the following NEP Reports:

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