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Bounds on expectations of small order statistics from decreasing density populations

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Abstract

For i > (n + 1)/2, Danielak (Statistics 37:305–324, 2003) established an optimal positive upper mean-variance bound on the expectation of ith order statistic based on the i.i.d. sample of size n from the decreasing density population. We show that the best bounds on the expected deviation of the ith order statistics from the population mean, i ≤ (n + 1)/2, expressed in more general scale units generated by pth absolute central moments with p > 1 amount to zero. We also determine the respective strictly negative bounds in the mean absolute deviation units.

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  1. Institute of Mathematics, Polish Academy of Sciences, Chopina 12, 87100, Toruń, Poland

    Tomasz Rychlik

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  1. Tomasz Rychlik
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Correspondence to Tomasz Rychlik.

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Rychlik, T. Bounds on expectations of small order statistics from decreasing density populations. Metrika 70, 369–381 (2009). https://doi.org/10.1007/s00184-008-0200-9

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  • DOI: https://doi.org/10.1007/s00184-008-0200-9

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