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A note on the Lynden-Bell estimator under association

Author

Listed:
  • Guessoum, Zohra
  • Ould Saïd, Elias
  • Sadki, Ourida
  • Tatachak, Abdelkader

Abstract

Let {XN,N≥1} be a stationary sequence of associated random variables of interest, and {YN,N≥1} be a sequence of random truncating variables assumed to be independent from {XN,N≥1}. In this paper, we establish strong uniform convergence with a rate of the well-known Lynden-Bell estimator under association hypothesis.

Suggested Citation

  • Guessoum, Zohra & Ould Saïd, Elias & Sadki, Ourida & Tatachak, Abdelkader, 2012. "A note on the Lynden-Bell estimator under association," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1994-2000.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:11:p:1994-2000
    DOI: 10.1016/j.spl.2012.06.016
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    References listed on IDEAS

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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. Doukhan, Paul & Louhichi, Sana, 1999. "A new weak dependence condition and applications to moment inequalities," Stochastic Processes and their Applications, Elsevier, vol. 84(2), pages 313-342, December.
    3. Sun, Liuquan & Zhou, Xian, 2001. "Survival function and density estimation for truncated dependent data," Statistics & Probability Letters, Elsevier, vol. 52(1), pages 47-57, March.
    4. Roussas, George G., 1991. "Kernel estimates under association: strong uniform consistency," Statistics & Probability Letters, Elsevier, vol. 12(5), pages 393-403, November.
    5. Pham, Tuan D. & Tran, Lanh T., 1985. "Some mixing properties of time series models," Stochastic Processes and their Applications, Elsevier, vol. 19(2), pages 297-303, April.
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    Cited by:

    1. Zohra Guessoum & Abdelkader Tatachak, 2020. "Asymptotic Results for Truncated-censored and Associated Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(1), pages 142-164, May.

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