Improving small-sample variance estimators for bounded random variables.

*(English)*Zbl 0637.62024Summary: This paper considers mean-square error (MSE) improvements in variance estimation for very small samples, typically from $n=2$ to $n=10$. The technique utilizes recent results in variance bounds for the truncation of traditional estimators. In many cases the improvement is based only on knowledge of the support of the sampled distribution and a weak characterization of its shape, and thus affords practical MSE reduction.

The extent of mean-square error reduction is investigated by using small samples from various simulated beta distributions. The technique is applied to Stein’s two-stage estimation procedure for the mean. The paper concludes with a comment on the no-data problem and applications.