New estimators of distribution functions

A. K. Md. Ehsanes Saleh and Amal Ghania

Communications in Statistics - Theory and Methods, 2016, vol. 45, issue 11, 3145-3157

Abstract: This article considers the estimation of a distribution function FX(x) based on a random sample X1, X2, …, Xn when the sample is suspected to come from a close-by distribution F0(x). The new estimators, namely the preliminary test (PTE) and Stein-type estimator (SE) are defined and compared with the “empirical distribution function” (edf) under local departure. In this case, we show that Stein-type estimators are superior to edf and PTE is superior to edf when it is close to F0(x). As a by-product similar estimators are proposed for population quantiles.

Date: 2016
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DOI: 10.1080/03610926.2014.897138

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