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MAXIMUM VARIANCE OF ORDER STATISTICS

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NICKOS PAPADATOS

*Department of Mathematics, Section of Statistics and
Operations
Research,*

University of Athens, Panepistemiopolis, 15784 Athens,
Greece
(Received June 30, 1993; revised May 17, 1994)

**Abstract.**
Yang (1982, *Bull. Inst. Math.
Acad. Sinica*, **10**(2), 197-204)
proved that the
variance of the sample median cannot exceed the population
variance. In this paper, the upper bound for the variance of order
statistics is derived, and it is shown that this is attained by
Bernoulli variates only. The proof is based on Hoeffding's identity
for the covariance.

*Key words and phrases*:
Variance bounds, order
statistics, Bernoulli variates, Hoeffding's identity.

**Source**
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