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The asymptotic theory of concomitants of order statistics

Published online by Cambridge University Press:  14 July 2016

H. A. David  and
J. Galambos
H. A. David
Affiliation:
Iowa State University, Ames
J. Galambos*
Affiliation:
Iowa State University, Ames
*
*Now at Temple University, Philadelphia.
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Abstract

In a random sample of n pairs (Xr, Yr), r = 1, 2, …, n, drawn from a bivariate normal distribution, let Xr:n be the rth order statistic among the Xr and let Y[r:n] be the Y-variate paired with Xr:n. The Y[r:n], which we call concomitants of the order statistics, arise most naturally in selection procedures based on the Xr:n. It is shown that asymptotically the k quantities k fixed, are independent, identically distributed variates. In addition, putting Rt,n for the number of integers j for which , the asymptotic distribution and all moments of n–1Rt, n are determined for t such that t/n → λ with 0 < λ < 1.

Keywords

BIVARIATE NORMALORDER STATISTICSCONCOMITANTSSELECTIONSRANKASYMPTOTIC DISTRIBUTIONSMOMENTSMULTIVARIATE NORMAL

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 11 , Issue 4 , December 1974 , pp. 762 - 770
Copyright
Copyright © Applied Probability Trust 1974 

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Footnotes

Parts of this paper were presented by the first named author at the 39th Session of the I. S. I., Vienna, 1973. The present work was supported by the Army Research Office — Durham.

References

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Rao, C. R. (1965) Linear Statistical Inference and its Applications. Wiley, New York.Google Scholar
Watterson, G. A. (1959) Linear estimation in censored samples from multivariate normal populations. Ann. Math. Statist. 30, 814–824.Google Scholar