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On discrete Epanechnikov kernel functions

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  • Chu, Chi-Yang
  • Henderson, Daniel J.
  • Parmeter, Christopher F.

Abstract

Least-squares cross-validation is commonly used for selection of smoothing parameters in the discrete data setting; however, in many applied situations, it tends to select relatively small bandwidths. This tendency to undersmooth is due in part to the geometric weighting scheme that many discrete kernels possess. This problem may be avoided by using alternative kernel functions. Specifically, discrete versions (both unordered and ordered) of the popular Epanechnikov kernel do not have rapidly decaying weights. The analytic properties of these kernels are contrasted with commonly used discrete kernel functions and their relative performance is compared using both simulated and real data. The simulation and empirical results show that these kernel functions generally perform well and in some cases demonstrate substantial gains in terms of mean squared error.

Suggested Citation

  • Chu, Chi-Yang & Henderson, Daniel J. & Parmeter, Christopher F., 2017. "On discrete Epanechnikov kernel functions," Computational Statistics & Data Analysis, Elsevier, vol. 116(C), pages 79-105.
    • Handle: RePEc:eee:csdana:v:116:y:2017:i:c:p:79-105
    DOI: 10.1016/j.csda.2017.07.003
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    References listed on IDEAS

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    1. Chi-Yang Chu & Daniel J. Henderson & Christopher F. Parmeter, 2015. "Plug-in Bandwidth Selection for Kernel Density Estimation with Discrete Data," Econometrics, MDPI, vol. 3(2), pages 1-16, March.
    2. Li, Degui & Simar, Léopold & Zelenyuk, Valentin, 2016. "Generalized nonparametric smoothing with mixed discrete and continuous data," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 424-444.
    3. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    4. Guerra, Rudy & Polansky, Alan M. & Schucany, William R., 1997. "Smoothed bootstrap confidence intervals with discrete data," Computational Statistics & Data Analysis, Elsevier, vol. 26(2), pages 163-176, December.
    5. Peter Hall & Andrew P. Robinson, 2009. "Reducing variability of crossvalidation for smoothing-parameter choice," Biometrika, Biometrika Trust, vol. 96(1), pages 175-186.
    6. 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.
    7. Li, Qi & Racine, Jeff, 2003. "Nonparametric estimation of distributions with categorical and continuous data," Journal of Multivariate Analysis, Elsevier, vol. 86(2), pages 266-292, August.
    8. Schremmer, Eckart, 1978. "Die Augsburger Steuerbücher um 1600. By Claus-Peter Clasen. Augsburg: Verlag Hieronymus Mühlberger, 1976. Pp. 64," The Journal of Economic History, Cambridge University Press, vol. 38(2), pages 524-525, June.
    9. Asparoukhov, Ognian K. & Krzanowski, Wojtek J., 2001. "A comparison of discriminant procedures for binary variables," Computational Statistics & Data Analysis, Elsevier, vol. 38(2), pages 139-160, December.
    10. 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.
    11. Su, Liangjun & Lu, Xun, 2013. "Nonparametric dynamic panel data models: Kernel estimation and specification testing," Journal of Econometrics, Elsevier, vol. 176(2), pages 112-133.
    12. QI Li & Jeff Racine, 2004. "Predictor relevance and extramarital affairs," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 19(4), pages 533-535.
    13. Qian, Junhui & Wang, Le, 2012. "Estimating semiparametric panel data models by marginal integration," Journal of Econometrics, Elsevier, vol. 167(2), pages 483-493.
    14. Jeffrey Racine, 2008. "Nonparametric econometrics: a primer (in Russian)," Quantile, Quantile, issue 4, pages 7-56, March.
    15. Peter Hall & Jeff Racine & Qi Li, 2004. "Cross-Validation and the Estimation of Conditional Probability Densities," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1015-1026, December.
    16. Henderson, Daniel J. & Carroll, Raymond J. & Li, Qi, 2008. "Nonparametric estimation and testing of fixed effects panel data models," Journal of Econometrics, Elsevier, vol. 144(1), pages 257-275, May.
    17. Racine, Jeffrey S., 2008. "Nonparametric Econometrics: A Primer," Foundations and Trends(R) in Econometrics, now publishers, vol. 3(1), pages 1-88, March.
    18. Coppejans, Mark, 2003. "Effective nonparametric estimation in the case of severely discretized data," Journal of Econometrics, Elsevier, vol. 117(2), pages 331-367, December.
    19. 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.
    20. Daniel J. Henderson & Subal C. Kumbhakar, 2006. "Public and Private Capital Productivity Puzzle: A Nonparametric Approach," Southern Economic Journal, John Wiley & Sons, vol. 73(1), pages 219-232, July.
    21. Clifford M. Hurvich & Jeffrey S. Simonoff & Chih‐Ling Tsai, 1998. "Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(2), pages 271-293.
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