TEST https://doi.org/10.1007/s11749-018-0588-0 ORIGINAL PAPER Prior-free probabilistic interval estimation for binomial proportion 1 1,2 1 Hezhi Lu · Hua Jin · Zhining Wang · 1 2,3,4 Chao Chen · Ying Lu Received: 17 November 2017 / Accepted: 14 May 2018 © Sociedad de Estadística e Investigación Operativa 2018 Abstract The interval estimation of a binomial proportion has been one of the most important problems in statistical inference. The modiﬁed Wilson interval, Agresti— Coull interval, and modiﬁed Jeffreys interval have good coverage probabilities among the existing methods. However, as approximation approaches, they still behave poorly under some circumstances. In this paper, we propose an exact and efﬁcient random- ized plausible interval based on the inference model and suggest the practical use of its non-randomized approximation. The randomized plausible interval is proven to have the exact coverage probability. Moreover, our non-randomized approximation is competitive with the existing approaches conﬁrmed by the simulation studies. Three examples including a real data analysis are illustrated to portray the usefulness of our method. Keywords Inferential model · Binomial proportion · Interval estimation · Coverage probability · Expected length Mathematics Subject Classiﬁcation 62F25 · 62P10 Hua Jin firstname.lastname@example.org School of Mathematical Science, South China Normal University, Guangzhou
TEST – Springer Journals
Published: Jun 5, 2018
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