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Note on the uniform convergence of density estimates for mixing random variables

Author

Listed:
  • Ioannides, D.
  • Roussas, G. G.

Abstract

On the basis of the random variables X1,...,Xn drawn from the (strictly) stationary and [phi]i-mixing (for some i = 1,...,4) stochastic process {Xn}, n [greater-or-equal, slanted] 1, a uniformly strongly consistent estimate of the (common) probability density function of the X's is constructed. For the case that the underlying process is also Markovian, uniformly strongly consistent estimates are constructed for the initial, the (X1, X2)-joint and the transition probability density functions of the process.

Suggested Citation

  • Ioannides, D. & Roussas, G. G., 1987. "Note on the uniform convergence of density estimates for mixing random variables," Statistics & Probability Letters, Elsevier, vol. 5(4), pages 279-285, June.
    • Handle: RePEc:eee:stapro:v:5:y:1987:i:4:p:279-285
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    Citations

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    Cited by:

    1. Hallin, Marc & Lu, Zudi & Tran, Lanh T., 2004. "Kernel density estimation for spatial processes: the L1 theory," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 61-75, January.
    2. Lu, Zudi & Chen, Xing, 2004. "Spatial kernel regression estimation: weak consistency," Statistics & Probability Letters, Elsevier, vol. 68(2), pages 125-136, June.
    3. 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.
    4. Carbon, Michel & Garel, Bernard & Tran, Lanh Tat, 1997. "Frequency polygons for weakly dependent processes," Statistics & Probability Letters, Elsevier, vol. 33(1), pages 1-13, April.
    5. Lanh Tran, 1990. "Recursive kernel density estimators under a weak dependence condition," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(2), pages 305-329, June.

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