Abstract
ABSTRACTThis 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.
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