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Nonparametric density estimation: A comparative study

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  • Teruko Takada

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    (Department of Economics, University of Illinois)

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    Abstract

    Motivated by finance applications, the objective of this paper is to assess the performance of several important methods for univariate density estimation focusing on the robustness of the methods to heavy tailed target densities. We consider four approaches: a fixed bandwidth kernel estimator, an adaptive bandwidth kernel estimator, the Hermite series (SNP) estimator of Gallant and Nychka, and the logspline estimator of Kooperberg and Stone. We conclude that the logspline and adaptive kernel methods are superior for fitting heavy tailed densities. Evaluation of the convergence rates of the SNP estimator for the family of Student-t densities reveals poor performance, measured by Hellinger error. In contrast, the logspline estimator exhibits good convergence independent of the tail behavior of the target density. These findings are confirmed in a small Monte-Carlo experiment.

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    Bibliographic Info

    Article provided by AccessEcon in its journal Economics Bulletin.

    Volume (Year): 3 (2001)
    Issue (Month): 16 ()
    Pages: 1-10

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    Handle: RePEc:ebl:ecbull:eb-01c10007

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    1. Baillie, Richard T & Bollerslev, Tim, 2002. "The Message in Daily Exchange Rates: A Conditional-Variance Tale," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 60-68, January.
    2. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-90, March.
    3. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
    4. Fenton, Victor M. & Gallant, A. Ronald, 1996. "Qualitative and asymptotic performance of SNP density estimators," Journal of Econometrics, Elsevier, vol. 74(1), pages 77-118, September.
    5. repec:fth:louvco:9205 is not listed on IDEAS
    6. Engle, Robert F & Gonzalez-Rivera, Gloria, 1991. "Semiparametric ARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(4), pages 345-59, October.
    7. Kooperberg, Charles & Stone, Charles J., 1991. "A study of logspline density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 12(3), pages 327-347, November.
    8. Coppejans, Mark & Gallant, A. Ronald, 2000. "Cross Validated SNP Density Estimates," Working Papers 00-10, Duke University, Department of Economics.
    9. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-47, August.
    10. Fenton, Victor M & Gallant, A Ronald, 1996. "Convergence Rates of SNP Density Estimators," Econometrica, Econometric Society, vol. 64(3), pages 719-27, May.
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    Cited by:
    1. Mittelhammer, Ron C. & Judge, George, 2011. "A family of empirical likelihood functions and estimators for the binary response model," Journal of Econometrics, Elsevier, vol. 164(2), pages 207-217, October.

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