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On deviations between empirical and quantile processes for mixing random variables

Author

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  • Babu, Gutti Jogesh
  • Singh, Kesar

Abstract

Let {Xn} be a strictly stationary [phi]-mixing process with [Sigma]j=1[infinity] [phi]1/2(j)

Suggested Citation

  • Babu, Gutti Jogesh & Singh, Kesar, 1978. "On deviations between empirical and quantile processes for mixing random variables," Journal of Multivariate Analysis, Elsevier, vol. 8(4), pages 532-549, December.
    • Handle: RePEc:eee:jmvana:v:8:y:1978:i:4:p:532-549
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    Citations

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    Cited by:

    1. Yu, Hao, 1996. "A note on strong approximation for quantile processes of strong mixing sequences," Statistics & Probability Letters, Elsevier, vol. 30(1), pages 1-7, September.
    2. Sun, Shuxia, 2006. "The Bahadur representation for sample quantiles under weak dependence," Statistics & Probability Letters, Elsevier, vol. 76(12), pages 1238-1244, July.
    3. Dagmara Dudek & Anna Kuczmaszewska, 2024. "Some practical and theoretical issues related to the quantile estimators," Statistical Papers, Springer, vol. 65(6), pages 3917-3933, August.
    4. Ouimet, Frédéric, 2021. "Asymptotic properties of Bernstein estimators on the simplex," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    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. Xuejun Wang & Yi Wu & Wei Yu & Wenzhi Yang & Shuhe Hu, 2019. "Asymptotics for the linear kernel quantile estimator," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(4), pages 1144-1174, December.
    7. Babu, G. Jogesh & Chaubey, Yogendra P., 2006. "Smooth estimation of a distribution and density function on a hypercube using Bernstein polynomials for dependent random vectors," Statistics & Probability Letters, Elsevier, vol. 76(9), pages 959-969, May.
    8. 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.
    9. Lanh Tran, 1988. "Rank order statistics for time series models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 40(2), pages 247-260, June.
    10. Wendler, Martin, 2011. "Bahadur representation for U-quantiles of dependent data," Journal of Multivariate Analysis, Elsevier, vol. 102(6), pages 1064-1079, July.
    11. Serinko, Regis J. & Babu, Gutti Jogesh, 1995. "Asymptotics of k-mean clustering under non-i.i.d. sampling," Statistics & Probability Letters, Elsevier, vol. 24(1), pages 57-66, July.
    12. Sharipov, Olimjon Sh. & Wendler, Martin, 2013. "Normal limits, nonnormal limits, and the bootstrap for quantiles of dependent data," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1028-1035.
    13. Yoshihara, Ken-ichi, 1995. "The Bahadur representation of sample quantiles for sequences of strongly mixing random variables," Statistics & Probability Letters, Elsevier, vol. 24(4), pages 299-304, September.
    14. Wendler, Martin, 2012. "U-processes, U-quantile processes and generalized linear statistics of dependent data," Stochastic Processes and their Applications, Elsevier, vol. 122(3), pages 787-807.
    15. Polonik, Wolfgang & Yao, Qiwei, 2002. "Set-Indexed Conditional Empirical and Quantile Processes Based on Dependent Data," Journal of Multivariate Analysis, Elsevier, vol. 80(2), pages 234-255, February.

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