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Extreme variances of order statistics in dependent samples

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  • Rychlik, Tomasz

Abstract

We determine optimal bounds on variances of order statistics based on samples of dependent identically distributed random variables in terms of population variance scale units.

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  • Rychlik, Tomasz, 2008. "Extreme variances of order statistics in dependent samples," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1577-1582, September.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:12:p:1577-1582
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    References listed on IDEAS

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    1. Nickos Papadatos, 1995. "Maximum variance of order statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(1), pages 185-193, January.
    2. Klimczak, Monika & Rychlik, Tomasz, 2004. "Maximum variance of Kth records," Statistics & Probability Letters, Elsevier, vol. 69(4), pages 421-430, October.
    3. Lin, G. D. & Huang, J. S., 1989. "Variances of sample medians," Statistics & Probability Letters, Elsevier, vol. 8(2), pages 143-146, June.
    4. Nagaraja, H. N. & Nevzorov, V. B., 1996. "Correlations between functions of records can be negative," Statistics & Probability Letters, Elsevier, vol. 29(2), pages 95-100, August.
    5. Papathanasiou, V., 1990. "Some characterizations of distributions based on order statistics," Statistics & Probability Letters, Elsevier, vol. 9(2), pages 145-147, February.
    6. Rychlik, Tomasz, 1994. "Distributions and expectations of order statistics for possibly dependent random variables," Journal of Multivariate Analysis, Elsevier, vol. 48(1), pages 31-42, January.
    7. Chunsheng, Ma, 1992. "Variance bound of function of order statistics," Statistics & Probability Letters, Elsevier, vol. 13(1), pages 25-27, January.
    8. Qi, Yong-cheng, 1994. "Some results on covariance of function of order statistics," Statistics & Probability Letters, Elsevier, vol. 19(2), pages 111-114, January.
    9. Li, Luning, 1994. "A counterexample to a conjecture on order statistics," Statistics & Probability Letters, Elsevier, vol. 19(2), pages 129-130, January.
    10. Nickos Papadatos, 1997. "A Note on Maximum Variance of Order Statistics from Symmetric Populations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(1), pages 117-121, March.
    11. Koiti Takahasi & Masao Futatsuya, 1998. "Dependence Between Order Statistics in Samples from Finite Population and its Application to Ranked Set Sampling," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(1), pages 49-70, March.
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    Cited by:

    1. Marek Beśka & Krzysztof Jasiński & Tomasz Rychlik & Marcin Spryszyński, 2012. "Mixed systems with minimal and maximal lifetime variances," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(7), pages 877-894, October.

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