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Estimation of the survival function for stationary associated processes

Author

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  • Bagai, Isha
  • Prakasa Rao, B. L. S.

Abstract

Let {Xn, n [greater-or-equal, slanted] 1} be a stationary sequence of associated random variables with survival function (x) = P[X1 > x]. The empirical survival function n(x) based on X1, X2,..., Xn is proposed as an estimator for (x). Strong consistency, pointwise as well as uniform, and asymptotic normality of n(x) are discussed.

Suggested Citation

  • Bagai, Isha & Prakasa Rao, B. L. S., 1991. "Estimation of the survival function for stationary associated processes," Statistics & Probability Letters, Elsevier, vol. 12(5), pages 385-391, November.
    • Handle: RePEc:eee:stapro:v:12:y:1991:i:5:p:385-391
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    Citations

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    Cited by:

    1. Ioannides, D. A. & Roussas, G. G., 1999. "Exponential inequality for associated random variables," Statistics & Probability Letters, Elsevier, vol. 42(4), pages 423-431, May.
    2. Roussas, George G., 1995. "Asymptotic normality of a smooth estimate of a random field distribution function under association," Statistics & Probability Letters, Elsevier, vol. 24(1), pages 77-90, July.
    3. Dewan, Isha & Rao, B.L.S. Prakasa, 2005. "Wilcoxon-signed rank test for associated sequences," Statistics & Probability Letters, Elsevier, vol. 71(2), pages 131-142, February.
    4. Cai, Zongwu & Roussas, George G., 1998. "Kaplan-Meier Estimator under Association," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 318-348, November.
    5. Garg, Mansi & Dewan, Isha, 2015. "On asymptotic behavior of U-statistics for associated random variables," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 209-220.
    6. Yi Wu & Wei Yu & Xuejun Wang, 2022. "Strong representations of the Kaplan–Meier estimator and hazard estimator with censored widely orthant dependent data," Computational Statistics, Springer, vol. 37(1), pages 383-402, March.
    7. Dewan, Isha & Rao, B. L. S. Prakasa, 2000. "Explicit bounds on Lévy-Prohorov distance for a class of multidimensional distribution functions," Statistics & Probability Letters, Elsevier, vol. 48(2), pages 105-119, June.
    8. Dudzinski, Marcin, 2008. "The almost sure central limit theorems in the joint version for the maxima and sums of certain stationary Gaussian sequences," Statistics & Probability Letters, Elsevier, vol. 78(4), pages 347-357, March.
    9. Roussas, George G., 2001. "An Esséen-type inequality for probability density functions, with an application," Statistics & Probability Letters, Elsevier, vol. 51(4), pages 397-408, February.
    10. Isha Bagai & B. Prakasa Rao, 1995. "Kernel-type density and failure rate estimation for associated sequences," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(2), pages 253-266, June.
    11. Isha Dewan & B. Rao, 2003. "Mann-Whitney test for associated sequences," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(1), pages 111-119, March.
    12. Li, Yongming & Yang, Shanchao & Wei, Chengdong, 2011. "Some inequalities for strong mixing random variables with applications to density estimation," Statistics & Probability Letters, Elsevier, vol. 81(2), pages 250-258, February.
    13. Isha Dewan & B. Rao, 1997. "Remarks on the strong law of large numbers for a triangular array of associated random variables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 45(1), pages 225-234, January.
    14. Yogendra P. Chaubey & Isha Dewan & Jun Li, 2021. "On Some Smooth Estimators of the Quantile Function for a Stationary Associated Process," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 114-139, May.
    15. Masry, Elias, 2003. "Local polynomial fitting under association," Journal of Multivariate Analysis, Elsevier, vol. 86(2), pages 330-359, August.
    16. Chaubey, Yogendra P. & Dewan, Isha & Li, Jun, 2011. "Smooth estimation of survival and density functions for a stationary associated process using Poisson weights," Statistics & Probability Letters, Elsevier, vol. 81(2), pages 267-276, February.

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