A Note on the Upper Bound to Variance of the Sample Extreme from a Finite Population

Abstract

We construct a new upper bound for the variance of the sample minimum and maximum in the case of a simple random sample drawn without replacement. The bound is optimal in the form provided. Similar bounds are shown for the other order statistics.

Keywords:

• Order statistic
• Sample spacings
• Sampling without replacement
• Hoeffding decomposition
• Finite population.

Mathematics Subject Classification:

• Primary 62G30
• Secondary 60E15.