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Estimation of the Asymptotic Variance of Kernel Density Estimators for Continuous Time Processes

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  • Guillou, Armelle
  • Merlevède, Florence

Abstract

In order to construct confidence sets for a marginal density f of a strictly stationary continuous time process observed over the time interval [0, T], it is necessary to have at one's disposal a Central Limit Theorem for the kernel density estimator fT. In this paper we address the question of nonparametric estimation of the asymptotic variance of  fT, an unknown quantity dependent on f. We construct two estimators and study their asymptotic properties.

Suggested Citation

  • Guillou, Armelle & Merlevède, Florence, 2001. "Estimation of the Asymptotic Variance of Kernel Density Estimators for Continuous Time Processes," Journal of Multivariate Analysis, Elsevier, vol. 79(1), pages 114-137, October.
    • Handle: RePEc:eee:jmvana:v:79:y:2001:i:1:p:114-137
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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.
    2. Bosq, Denis & Merlevède, Florence & Peligrad, Magda, 1999. "Asymptotic Normality for Density Kernel Estimators in Discrete and Continuous Time," Journal of Multivariate Analysis, Elsevier, vol. 68(1), pages 78-95, January.
    3. Kutoyants, Yu. A., 1997. "Some problems of nonparametric estimation by observations of ergodic diffusion process," Statistics & Probability Letters, Elsevier, vol. 32(3), pages 311-320, March.
    4. Politis, Dimitris N. & Romano, Joseph P., 1993. "On the sample variance of linear statistics derived from mixing sequences," Stochastic Processes and their Applications, Elsevier, vol. 45(1), pages 155-167, March.
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    Cited by:

    1. 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.

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