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Asymptotic Normality for Density Kernel Estimators in Discrete and Continuous Time

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  • Bosq, Denis
  • Merlevède, Florence
  • Peligrad, Magda

Abstract

In this paper, we build a central limit theorem for triangular arrays of sequences which satisfy a mild mixing condition. This result allows us to study asymptotic normality of density kernel estimators for some classes of continuous and discrete time processes.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:68:y:1999:i:1:p:78-95
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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. Bradley, Richard C., 1983. "Asymptotic normality of some kernel-type estimators of probability density," Statistics & Probability Letters, Elsevier, vol. 1(6), pages 295-300, October.
    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.
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    Cited by:

    1. Nadia Bensaïd & Sophie Dabo-Niang, 2010. "Frequency polygons for continuous random fields," Statistical Inference for Stochastic Processes, Springer, vol. 13(1), pages 55-80, April.
    2. Kanaya, Shin, 2017. "Convergence Rates Of Sums Of Α-Mixing Triangular Arrays: With An Application To Nonparametric Drift Function Estimation Of Continuous-Time Processes," Econometric Theory, Cambridge University Press, vol. 33(5), pages 1121-1153, October.
    3. 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.
    4. Wang, Yizao & Woodroofe, Michael, 2014. "On the asymptotic normality of kernel density estimators for causal linear random fields," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 201-213.
    5. Longla, Martial & Peligrad, Magda & Sang, Hailin, 2015. "On kernel estimators of density for reversible Markov chains," Statistics & Probability Letters, Elsevier, vol. 100(C), pages 149-157.
    6. Mohamed El Machkouri, 2013. "On the asymptotic normality of frequency polygons for strongly mixing spatial processes," Statistical Inference for Stochastic Processes, Springer, vol. 16(3), pages 193-206, 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.
    8. Lei, Liangzhen & Wu, Liming, 2005. "Large deviations of kernel density estimator in L1(Rd) for uniformly ergodic Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 115(2), pages 275-298, February.
    9. Mohamed El Machkouri, 2011. "Asymptotic normality of the Parzen–Rosenblatt density estimator for strongly mixing random fields," Statistical Inference for Stochastic Processes, Springer, vol. 14(1), pages 73-84, February.

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