Estimation of Variance Using Judgment Ordered Ranked Set Samples

Ranked set sampling has been shown by Dell and Clutter (1972, Biometrics 28, 545-553) to be a useful technique for improving estimates of the mean when actual measurement of the observations is diflicult but ranking of the elements in a sample is relatively easy. The technique is extended here to show an estimator of variance, which is asymptotically unbiased regardless of the presence of errors in ranking. Furthermore, the asymptotic efficiency of these estimators, relative to those based on the same number of quantified observations from a random sample, is greater than unity for any underlying distribution, even if ranking errors occur.