Admissibility of the Empirical Distribution Function in discrete nonparametric invariant problems

Qiqing Yu

Statistics & Probability Letters, 1993, vol. 18, issue 5, 337-343

Abstract: Consider nonparametric problems of estimating an unknown distribution function, F, under the loss L(F,a)=[integral operator] F(t)-a(t)2(F(t))[alpha](1 -F(t))[beta]dF(t), where [alpha][set membership, variant][-1,0] and [beta][set membership, variant][-1,1]. It is proved that the Empirical Distribution Function (EDF) is admissible (extending a result of Brown, 1988). Among them, an important case is the loss L(F,a)=[integral operator]F(t)- a(t)2dF(t).

Keywords: Admissibility; invariant; estimator; nonparametric; estimator; discrete; distribution; stepwise; Bayes; procedure (search for similar items in EconPapers)
Date: 1993
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