Admissibility of the Empirical Distribution Function in discrete nonparametric invariant problems

Qiqing Yu

doi:10.1016/0167-7152(93)90025-E

Admissibility of the Empirical Distribution Function in discrete nonparametric invariant problems

Qiqing Yu

Mathematics and Statistics

Binghamton University

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Consider nonparametric problems of estimating an unknown distribution function, F, under the loss L(F,a)=∫| F(t)-a(t)|²(F(t))^α(1 -F(t))^βdF(t), where α∈[-1,0] and β∈[-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)=∫|F(t)- a(t)|²dF(t).

Original language	English
Pages (from-to)	337-343
Number of pages	7
Journal	Statistics and Probability Letters
Volume	18
Issue number	5
DOIs	https://doi.org/10.1016/0167-7152(93)90025-E
State	Published - Dec 2 1993

Keywords

Admissibility
discrete distribution
invariant estimator
nonparametric estimator
stepwise Bayes procedure

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10.1016/0167-7152(93)90025-E

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abstract = "Consider nonparametric problems of estimating an unknown distribution function, F, under the loss L(F,a)=∫| F(t)-a(t)|2(F(t))α(1 -F(t))βdF(t), where α∈[-1,0] and β∈[-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)=∫|F(t)- a(t)|2dF(t).",

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N2 - Consider nonparametric problems of estimating an unknown distribution function, F, under the loss L(F,a)=∫| F(t)-a(t)|2(F(t))α(1 -F(t))βdF(t), where α∈[-1,0] and β∈[-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)=∫|F(t)- a(t)|2dF(t).

AB - Consider nonparametric problems of estimating an unknown distribution function, F, under the loss L(F,a)=∫| F(t)-a(t)|2(F(t))α(1 -F(t))βdF(t), where α∈[-1,0] and β∈[-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)=∫|F(t)- a(t)|2dF(t).

KW - Admissibility

KW - discrete distribution

KW - invariant estimator

KW - nonparametric estimator

KW - stepwise Bayes procedure

UR - https://www.scopus.com/pages/publications/38248999510

U2 - 10.1016/0167-7152(93)90025-E

DO - 10.1016/0167-7152(93)90025-E

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SP - 337

EP - 343

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 5

ER -

Admissibility of the Empirical Distribution Function in discrete nonparametric invariant problems

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Keywords

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