Student's t Approximations for Three Simple Robust Estimators

原文摘要

Suppose that Tn is an estimator of a location parameter θ, Sn is an estimator of its standard error, and both are based on a random sample of size n. Then, approximations of (Tn – θ)/Sn in terms of Student's t are convenient and useful in confidence-interval estimation and tests of hypotheses of θ. In this article some moment-based t approximations of studentized trimmed means, the trimean, and Gastwirth's estimator are constructed at the normal and several near-normal parents, and compared with some earlier t approximations closely associated with Tukey's jackknife and an approach of Huber (1970). The latter two approximations are based on conjectures involving the large-sample distributional behavior of Tn and Sn , whereas for the new approximations, the moments are computed using Monte Carlo techniques. The trimmed means, trimean, and Gastwirth's estimator are studentized by using the Winsorized standard deviations, the interquartile range, and the intertertile range, respectively. The moment-based t approximations are observed to compare favorably over the earlier proposals and consequently the method of construction may have wider applicability. Finally, with consideration given to the robustness aspect in data analysis, certain finite-sample definitions of the studentizations and their overall appropriate t approximations are found, and their superiority over the usual Student-t statistic in confidence-interval estimation and hypothesis testing is observed.

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