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Asymptotic behavior of proportions of observations falling to random regions determined by central order statistics

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  • Augustynowicz, Aneta

Abstract

In this paper, we present a new version of strong ergodic theorem for proportions of observations in a sample falling to a random region determined by a given Borel set and central order statistics. It will be a refinement of a previous result which provides conditions sufficient for the almost sure convergence of such sequence and gives the description of its limit.

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  • Augustynowicz, Aneta, 2020. "Asymptotic behavior of proportions of observations falling to random regions determined by central order statistics," Statistics & Probability Letters, Elsevier, vol. 162(C).
    • Handle: RePEc:eee:stapro:v:162:y:2020:i:c:s016771522030047x
    DOI: 10.1016/j.spl.2020.108744
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    References listed on IDEAS

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    1. Ghosh, Yashowanto N. & Mukherjee, Bhramar, 2006. "On probabilistic properties of conditional medians and quantiles," Statistics & Probability Letters, Elsevier, vol. 76(16), pages 1775-1780, October.
    2. Dembinska, Anna & Iliopoulos, George, 2012. "On the asymptotics of numbers of observations in random regions determined by order statistics," Journal of Multivariate Analysis, Elsevier, vol. 103(1), pages 151-160, January.
    3. Enkelejd Hashorva & Claudio Macci & Barbara Pacchiarotti, 2013. "Large Deviations for Proportions of Observations Which Fall in Random Sets Determined by Order Statistics," Methodology and Computing in Applied Probability, Springer, vol. 15(4), pages 875-896, December.
    4. Hashorva, Enkelejd, 2004. "Bivariate maximum insurance claim and related point processes," Statistics & Probability Letters, Elsevier, vol. 69(2), pages 117-128, August.
    5. Li, Y. & Pakes, Anthony G., 2001. "On the number of near-maximum insurance claims," Insurance: Mathematics and Economics, Elsevier, vol. 28(3), pages 309-323, June.
    6. Pakes, Anthony G. & Li, Yun, 1998. "Limit laws for the number of near maxima via the Poisson approximation," Statistics & Probability Letters, Elsevier, vol. 40(4), pages 395-401, November.
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