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Smooth estimate of quantiles under association

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  • Cai, Zongwu
  • Roussas, George G.

Abstract

Let X1,X2,... be real-valued random variables forming a strictly stationary sequence, and satisfying the basic requirement of being positively or negatively associated. Let [xi]p denote the pth quantile of the marginal distribution function of the Xi's, which is estimated by a smooth (kernel-type) estimate , on the basis of the segment X1,..., Xn. The main results of this paper are those of establishing pointwise consistency, asymptotic normality with rates, and weak convergence of a stochastic process generated by .

Suggested Citation

  • Cai, Zongwu & Roussas, George G., 1997. "Smooth estimate of quantiles under association," Statistics & Probability Letters, Elsevier, vol. 36(3), pages 275-287, December.
    • Handle: RePEc:eee:stapro:v:36:y:1997:i:3:p:275-287
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    References listed on IDEAS

    as
    1. Ralescu, Stefan S., 1992. "A remainder estimate for the normal approximation of perturbed sample quantiles," Statistics & Probability Letters, Elsevier, vol. 14(4), pages 293-298, July.
    2. Roussas, George G., 1991. "Kernel estimates under association: strong uniform consistency," Statistics & Probability Letters, Elsevier, vol. 12(5), pages 393-403, November.
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    Cited by:

    1. É. Youndjé, 2022. "L1 Properties of the Nadaraya Quantile Estimator," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 867-884, August.
    2. Ioannides, D. A. & Roussas, G. G., 1999. "Exponential inequality for associated random variables," Statistics & Probability Letters, Elsevier, vol. 42(4), pages 423-431, May.
    3. Lihong Wang, 2010. "Kernel type smoothed quantile estimation under long memory," Statistical Papers, Springer, vol. 51(1), pages 57-67, January.
    4. K. Cheung & Stephen Lee, 2010. "Bootstrap variance estimation for Nadaraya quantile estimator," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(1), pages 131-145, May.
    5. Ling, Nengxiang, 2008. "The Bahadur representation for sample quantiles under negatively associated sequence," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2660-2663, November.
    6. Qinchi Zhang & Wenzhi Yang & Shuhe Hu, 2014. "On Bahadur representation for sample quantiles under α-mixing sequence," Statistical Papers, Springer, vol. 55(2), pages 285-299, May.
    7. Roussas, George G., 2000. "Asymptotic normality of the kernel estimate of a probability density function under association," Statistics & Probability Letters, Elsevier, vol. 50(1), pages 1-12, October.
    8. Youndjé, É. & Vieu, P., 2006. "A note on quantile estimation for long-range dependent stochastic processes," Statistics & Probability Letters, Elsevier, vol. 76(2), pages 109-116, January.
    9. Masry, Elias, 2002. "Multivariate probability density estimation for associated processes: strong consistency and rates," Statistics & Probability Letters, Elsevier, vol. 58(2), pages 205-219, June.
    10. Masry, Elias, 2003. "Local polynomial fitting under association," Journal of Multivariate Analysis, Elsevier, vol. 86(2), pages 330-359, August.
    11. Chen Jia & Zhang Lixin & Li Degui, 2008. "Spatial local M-estimation under association," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 67(1), pages 11-29, January.

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