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On the asymptotic variance of the continuous-time kernel density estimator

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  • Sköld, Martin
  • Hössjer, Ola

Abstract

We reformulate the conditions of Blanke and Bosq (1997) for achieving the (log T)/T-rate of convergence of the kernel density estimator for a smooth process and give under slightly stronger assumptions the exact asymptotic form of the variance giving an expression for the asymptotic optimal bandwidth. Conditions for the full T-1 and discrete-time rates are also considered.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:44:y:1999:i:1:p:97-106
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    References listed on IDEAS

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    1. 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.
    2. 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. D. Blanke, 2002. "Estimation of Local Smoothness Coefficients for Continuous Time Processes," Statistical Inference for Stochastic Processes, Springer, vol. 5(1), pages 65-93, January.
    2. 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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