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Multivariate probability density estimation for associated processes: strong consistency and rates

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  • Masry, Elias
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    Abstract

    We consider the estimation of the multivariate probability density function f(x1,...,xd) of X1,...,Xd of a stationary associated random process {Xi}i=-[infinity][infinity]. Uniform strong rates of convergence over compact sets in are established for the estimates of f and all its partial derivatives up to a given order s.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 58 (2002)
    Issue (Month): 2 (June)
    Pages: 205-219

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    Handle: RePEc:eee:stapro:v:58:y:2002:i:2:p:205-219

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    Keywords: Multivariate probability density estimation Associated processes Rates of strong convergence;

    References

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    1. Cai, Zongwu & Roussas, George G., 1998. "Kaplan-Meier Estimator under Association," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 318-348, November.
    2. Cai, Zongwu & Roussas, George G., 1997. "Smooth estimate of quantiles under association," Statistics & Probability Letters, Elsevier, Elsevier, vol. 36(3), pages 275-287, December.
    3. Roussas, George G., 2000. "Asymptotic normality of the kernel estimate of a probability density function under association," Statistics & Probability Letters, Elsevier, Elsevier, vol. 50(1), pages 1-12, October.
    4. Masry, Elias, 1989. "Nonparametric estimation of conditional probability densities and expectations of stationary processes: strong consistency and rates," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 32(1), pages 109-127, June.
    5. Roussas, George G., 1991. "Kernel estimates under association: strong uniform consistency," Statistics & Probability Letters, Elsevier, Elsevier, vol. 12(5), pages 393-403, November.
    6. Roussas, George G., 1995. "Asymptotic normality of a smooth estimate of a random field distribution function under association," Statistics & Probability Letters, Elsevier, Elsevier, vol. 24(1), pages 77-90, July.
    7. Masry, Elias, 1996. "Multivariate regression estimation local polynomial fitting for time series," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 65(1), pages 81-101, December.
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