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Determining the Number of Effective Parameters in Kernel Density Estimation

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  • McCloud, Nadine
  • Parmeter, Christopher F.

Abstract

The hat matrix maps the vector of response values in a regression to its predicted counterpart. The trace of this hat matrix is the workhorse for calculating the effective number of parameters in both parametric and nonparametric regression settings. Drawing on the regression literature, the standard kernel density estimate is transformed to mimic a regression estimate thus allowing extraction of a usable hat matrix for calculating the effective number of parameters of the kernel density estimate. Asymptotic expressions for the trace of this hat matrix are derived under standard regularity conditions for mixed, continuous, and discrete densities. Simulations validate the theoretical contributions. Several empirical examples demonstrate the usefulness of the method suggesting that calculating the effective number of parameters of a kernel density estimator maybe useful in interpreting differences across estimators.

Suggested Citation

  • McCloud, Nadine & Parmeter, Christopher F., 2020. "Determining the Number of Effective Parameters in Kernel Density Estimation," Computational Statistics & Data Analysis, Elsevier, vol. 143(C).
    • Handle: RePEc:eee:csdana:v:143:y:2020:i:c:s0167947319301987
    DOI: 10.1016/j.csda.2019.106843
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    References listed on IDEAS

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    1. Linton, Oliver & Xiao, Zhijie, 2007. "A Nonparametric Regression Estimator That Adapts To Error Distribution Of Unknown Form," Econometric Theory, Cambridge University Press, vol. 23(3), pages 371-413, June.
    2. Gerfin, Michael, 1996. "Parametric and Semi-parametric Estimation of the Binary Response Model of Labor Market Participation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(3), pages 321-339, May-June.
    3. Zhang, Chunming, 2003. "Calibrating the Degrees of Freedom for Automatic Data Smoothing and Effective Curve Checking," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 609-628, January.
    4. Li, Qi & Ouyang, Desheng, 2005. "Uniform convergence rate of kernel estimation with mixed categorical and continuous data," Economics Letters, Elsevier, vol. 86(2), pages 291-296, February.
    5. 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.
    6. Gozalo, Pedro & Linton, Oliver, 2000. "Local nonlinear least squares: Using parametric information in nonparametric regression," Journal of Econometrics, Elsevier, vol. 99(1), pages 63-106, November.
    7. Nadine McCloud & Christopher F. Parmeter, 2017. "Calculating Degrees of Freedom in Multivariate Local Polynomial Regression," Working Papers 2017-14, University of Miami, Department of Economics.
    8. Henderson,Daniel J. & Parmeter,Christopher F., 2015. "Applied Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521279680, November.
    9. Ao Yuan & Jan G. De Gooijer, 2007. "Semiparametric Regression with Kernel Error Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(4), pages 841-869, December.
    10. Hayfield, Tristen & Racine, Jeffrey S., 2008. "Nonparametric Econometrics: The np Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i05).
    11. Henderson Daniel J. & Parmeter Christopher F., 2017. "Root-n Consistent Kernel Density Estimation in Practice," Journal of Econometric Methods, De Gruyter, vol. 6(1), pages 1-10, January.
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    Cited by:

    1. Kirkby, J. Lars & Leitao, Álvaro & Nguyen, Duy, 2021. "Nonparametric density estimation and bandwidth selection with B-spline bases: A novel Galerkin method," Computational Statistics & Data Analysis, Elsevier, vol. 159(C).

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