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Accurate rates of density estimators for continuous-time processes

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  • Blanke, D.
  • Bosq, D.

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.

Suggested Citation

  • Blanke, D. & Bosq, D., 1997. "Accurate rates of density estimators for continuous-time processes," Statistics & Probability Letters, Elsevier, vol. 33(2), pages 185-191, April.
    • Handle: RePEc:eee:stapro:v:33:y:1997:i:2:p:185-191
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    References listed on IDEAS

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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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    1. Labrador, Boris, 2008. "Strong pointwise consistency of the kT -occupation time density estimator," Statistics & Probability Letters, Elsevier, vol. 78(9), pages 1128-1137, July.
    2. 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.
    3. D. Blanke & B. Pumo, 2003. "Optimal sampling for density estimation in continuous time," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(1), pages 1-23, January.
    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;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 321-342, June.
    5. 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.
    6. 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.
    7. 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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