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Zbl 0637.62024
Seaman, John W.jun.; Young, Dean M.; Odell, Patrick L.
Improving small-sample variance estimators for bounded random variables. (English)
[J] Ind. Math. 37, 65-75 (1987). ISSN 0019-8528

Summary: 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. \par 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.

MSC 2000:: *62F10 Point estimation
62G05 Nonparametric estimation

Keywords: bounded random variables; simulation results; variance estimation; very small samples; variance bounds; truncation; MSE; mean-square error reduction; beta distributions; Stein's two-stage estimation procedure; no-data problem

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