A Note on Quantile Estimation for Curtailed Experiments

Abstract

AbstractThere may be experiments where due to misadventure or logistic or ethical reasons final measurements on all experimental units cannot be obtained. If at least 50% of the final measurements have been taken estimates of the lower quantiles and the median can be obtained. For such curtailed experiments it is shown how quantiles, above those that can be estimated directly from the data set, can be estimated indirectly by exploiting a property of symmetric distributions. The performance of the indirect quantile estimator is compared with that of the direct quantile estimator and conditions for the indirect estimator to have smaller variance than the direct estimator are presented. It is also shown how the indirect estimator may be pooled with the direct estimator to obtain an improved estimate of the upper quantiles.When it cannot be assumed that the data come from a symmetric distribution transformations to symmetry may be performed and the indirect estimation technique used on the transformed data; back transformations then yield the estimates of the upper quantiles.