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Projection Method for Moment Bounds on Order Statistics from Restricted Families: I. Dependent Case


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  • Gajek, Leslaw
  • Rychlik, Tomasz
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    We present a method of projections onto convex cones for establishing the sharp bounds in terms of the first two moments for the expectations ofL-estimates based on samples from restricted families. In this part, we consider the case of possibly dependent identically distributed parent random variables. For the classes of decreasing failure probability, DFR, and symmetric unimodal marginal distributions, we first determine parametric subclasses which contain the distributions attaining the extreme expectations for allL-estimates. Then we derive the bounds for single order statistics. The results provide some new characterizations of uniform and exponential distributions

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 57 (1996)
    Issue (Month): 1 (April)
    Pages: 156-174

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    Handle: RePEc:eee:jmvana:v:57:y:1996:i:1:p:156-174

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    Keywords: dependent identically distributed random variables decreasing failure probability distribution decreasing failure rate distribution symmetric unimodal distribution uniform distribution exponential distribution L-estimate order statistic convex cone projection (null);


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    Cited by:
    1. Gajek, Leslaw & Rychlik, Tomasz, 1998. "Projection Method for Moment Bounds on Order Statistics from Restricted Families, : II. Independent Case," Journal of Multivariate Analysis, Elsevier, vol. 64(2), pages 156-182, February.
    2. Danielak, Katarzyna & Rychlik, Tomasz, 2003. "Sharp bounds for expectations of spacings from DDA and DFRA families," Statistics & Probability Letters, Elsevier, vol. 65(4), pages 303-316, December.
    3. Rychlik, Tomasz, 2002. "Best upper quantile evaluations for NWU distributions," Statistics & Probability Letters, Elsevier, vol. 58(2), pages 175-184, June.


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