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Accurate rates of density estimators for continuous-time processes

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  • Blanke, D.
  • Bosq, D.
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    Abstract

    We specify necessary conditions for getting parametric convergence rate of kernel density estimators. For continuous-time processes observed over [0, T], we show that two possible exact rates are (ln T)/T and 1/T, according to the nature of sample paths.

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    File URL: http://www.sciencedirect.com/science/article/B6V1D-3WNMX5B-V/2/e5fbf1d00f737d649e890eaa3a78f944
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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 33 (1997)
    Issue (Month): 2 (April)
    Pages: 185-191

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    Handle: RePEc:eee:stapro:v:33:y:1997:i:2:p:185-191

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    Related research

    Keywords: Nonparametric estimation Superoptimal rate Continuous-time process Kernel density estimator;

    References

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    1. Castellana, J. V. & Leadbetter, M. R., 1986. "On smoothed probability density estimation for stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 21(2), pages 179-193, February.
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    Cited by:
    1. Sköld, Martin & Hössjer, Ola, 1999. "On the asymptotic variance of the continuous-time kernel density estimator," Statistics & Probability Letters, Elsevier, vol. 44(1), pages 97-106, August.
    2. Llop, P. & Forzani, L. & Fraiman, R., 2011. "On local times, density estimation and supervised classification from functional data," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 73-86, January.
    3. Blanke, Delphine & Vial, Céline, 2008. "Assessing the number of mean square derivatives of a Gaussian process," Stochastic Processes and their Applications, Elsevier, vol. 118(10), pages 1852-1869, October.
    4. Liliana Forzani & Ricardo Fraiman & Pamela Llop, 2013. "Density estimation for spatial-temporal models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 22(2), pages 321-342, June.
    5. M. Sköld, 2001. "The Asymptotic Variance of the Continuous-Time Kernel Estimator with Applications to Bandwidth Selection," Statistical Inference for Stochastic Processes, Springer, vol. 4(1), pages 99-117, January.

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