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p-Norm bounds on the expectation of the maximum of a possibly dependent sample

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  • Arnold, Barry C.

Abstract

Let X1, X2,..., Xn be identically distributed possibly dependent random variables with finite pth absolute moment assumed without loss of generality to be equal to 1. Denote the order statistics by X1:n, X2:n,..., Xn:n. Bounds are derived for E(Xn:n) when it is assumed that the Xi's are (i) arbitrarily dependent and (ii) independent. The effect of assuming a symmetric common distribution for the Xi's is discussed. Analogous bounds are described for the expected range of the sample. Bounds on expectations of general linear combinations of order statistics are described in the independent case.

Suggested Citation

  • Arnold, Barry C., 1985. "p-Norm bounds on the expectation of the maximum of a possibly dependent sample," Journal of Multivariate Analysis, Elsevier, vol. 17(3), pages 316-332, December.
    • Handle: RePEc:eee:jmvana:v:17:y:1985:i:3:p:316-332
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    Cited by:

    1. Brandts, Jordi & El Baroudi, Sabrine & Huber, Stefanie J. & Rott, Christina, 2021. "Gender differences in private and public goal setting," Journal of Economic Behavior & Organization, Elsevier, vol. 192(C), pages 222-247.
    2. Raqab, Mohammad Z., 2010. "Evaluations of the mean residual lifetime of an m-out-of-n system," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 333-342, March.
    3. Tomasz Rychlik, 2014. "Non-positive upper bounds on expectations of small order statistics from DDA and DFRA populations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(4), pages 539-557, May.
    4. Lukas Hoesch & Adam Lee & Geert Mesters, 2022. "Robust inference for non-Gaussian SVAR models," Economics Working Papers 1847, Department of Economics and Business, Universitat Pompeu Fabra.
    5. Lukas Hoesch & Adam Lee & Geert Mesters, 2022. "Locally Robust Inference for Non-Gaussian SVAR Models," Working Papers 1367, Barcelona School of Economics.
    6. Huang, J. S., 1998. "Sequence of expectations of maximum-order statistics," Statistics & Probability Letters, Elsevier, vol. 38(2), pages 117-123, June.
    7. Tomasz Rychlik, 2001. "Stability of Order Statistics under Dependence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(4), pages 877-894, December.
    8. Rychlik, Tomasz, 2009. "Tight evaluations for expectations of small order statistics from symmetric and symmetric unimodal populations," Statistics & Probability Letters, Elsevier, vol. 79(12), pages 1488-1493, June.
    9. Z. Raqab, Mohammad, 2003. "P-Norm bounds for moments of progressive type II censored order statistics," Statistics & Probability Letters, Elsevier, vol. 64(4), pages 393-402, October.

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