Nonparametric density estimation: A comparative study
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.
Volume (Year): 3 (2001)
Issue (Month): 16 ()
|Contact details of provider:|| |
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- Baillie, Richard T & Bollerslev, Tim, 1989. "The Message in Daily Exchange Rates: A Conditional-Variance Tale," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(3), pages 297-305, July.
- Tom Doan, "undated". "RATS program to replicate Baillie and Bollerslev GARCH models with day-of-week effects," Statistical Software Components RTZ00172, Boston College Department of Economics.
- Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-390, March.
- Kooperberg, Charles & Stone, Charles J., 1991. "A study of logspline density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 12(3), pages 327-347, November.
- 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.
- Victor Fenton & Gallant, A. Ronald, 1996. "Qualitative and Asymptotic Performance of SNP Density Estimators," Working Papers 96-17, Duke University, Department of Economics.
- Fenton, Victor M & Gallant, A Ronald, 1996. "Convergence Rates of SNP Density Estimators," Econometrica, Econometric Society, vol. 64(3), pages 719-727, May.
- Coppejans, Mark & Gallant, A. Ronald, 2002. "Cross-validated SNP density estimates," Journal of Econometrics, Elsevier, vol. 110(1), pages 27-65, September.
- Coppejans, Mark & Gallant, A. Ronald, 2000. "Cross Validated SNP Density Estimates," Working Papers 00-10, Duke University, Department of Economics.
- 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.
- 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 542-547, August.
- Engle, Robert F & Gonzalez-Rivera, Gloria, 1991. "Semiparametric ARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(4), pages 345-359, October. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:ebl:ecbull:eb-01c10007. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (John P. Conley)
If references are entirely missing, you can add them using this form.