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Kernel density estimation under dependence

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  • Tran, Lanh Tat

Abstract

Kernel type estimators of the density of weakly dependent random variables are studied. Uniform strong consistency of the estimators and their rates of convergence are obtained. The dependence condition used is weaker than the strong mixing condition.

Suggested Citation

  • Tran, Lanh Tat, 1990. "Kernel density estimation under dependence," Statistics & Probability Letters, Elsevier, vol. 10(3), pages 193-201, August.
    • Handle: RePEc:eee:stapro:v:10:y:1990:i:3:p:193-201
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    Citations

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    Cited by:

    1. Liebscher E., 2001. "Estimation Of The Density And The Regression Function Under Mixing Conditions," Statistics & Risk Modeling, De Gruyter, vol. 19(1), pages 9-26, January.
    2. Liebscher, Eckhard, 1999. "Asymptotic normality of nonparametric estimators under [alpha]-mixing condition," Statistics & Probability Letters, Elsevier, vol. 43(3), pages 243-250, July.
    3. Liebscher, Eckhard, 1996. "Strong convergence of sums of [alpha]-mixing random variables with applications to density estimation," Stochastic Processes and their Applications, Elsevier, vol. 65(1), pages 69-80, December.
    4. Masry, Elias, 1997. "Multivariate probability density estimation by wavelet methods: Strong consistency and rates for stationary time series," Stochastic Processes and their Applications, Elsevier, vol. 67(2), pages 177-193, May.
    5. Leblanc, Frédérique, 1996. "Wavelet linear density estimator for a discrete-time stochastic process: Lp-losses," Statistics & Probability Letters, Elsevier, vol. 27(1), pages 71-84, March.
    6. Masry, Elias, 2011. "The estimation of the correlation coefficient of bivariate data under dependence: Convergence analysis," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1039-1045, August.
    7. Hwang, Eunju & Shin, Dong Wan, 2012. "Stationary bootstrap for kernel density estimators under ψ-weak dependence," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1581-1593.

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