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Covariance between variables and their order statistics for multivariate normal variables

Author

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  • Rinott, Yosef
  • Samuel-Cahn, Ester

Abstract

Siegel (1993, J. Amer. Statist. Assoc. 88, 77-80) showed that when (X1, ..., Xn) have a multivariate normal distribution then Cov(X1, X(1)) = [Sigma]ni = 1 Cov(X1, Xi)P(Xi = X(1)), where X(1) is the minimum of (X1, ..., Xn). We show that a similar result holds for any order statistic. Thus X(1) can be replaced by X(r), the rth order statistic, everywhere in the above formula. Normality is essentially also necessary for this result to hold.

Suggested Citation

  • Rinott, Yosef & Samuel-Cahn, Ester, 1994. "Covariance between variables and their order statistics for multivariate normal variables," Statistics & Probability Letters, Elsevier, vol. 21(2), pages 153-155, September.
    • Handle: RePEc:eee:stapro:v:21:y:1994:i:2:p:153-155
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    Cited by:

    1. Vitale, Richard A., 1996. "Covariance identities for normal variables via convex polytopes," Statistics & Probability Letters, Elsevier, vol. 30(4), pages 363-368, November.

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