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VOL. 57 | 2009 On the Estimation of Symmetric Distributions under Peakedness Order Constraints


Consider distribution functions F and G and suppose that F is more peaked about a than G is about b. The problem of estimating F or G, or both, when F and G are symmetric, arises quite naturally in applications. The empirical distribution functions Fn and Gm will not necessarily satisfy the order constraint imposed by the experimental conditions. Rojo and Batun-Cutz [Series in Biostatistics vol. 3, Advances in Statistical Modeling and Inference, (2007) 649–670] proposed some estimators that are strongly uniformly consistent when both m and n tend to infinity. However the estimators fail to be consistent when only either m or n tend to infinity. Here estimators are proposed that circumvent these problems and the asymptotic distribution of the estimators is delineated. A simulation study compares these estimators in terms of Mean Squared Error and Bias behavior with their competitors.


Published: 1 January 2009
First available in Project Euclid: 3 August 2009

zbMATH: 1271.62076
MathSciNet: MR2681662

Digital Object Identifier: 10.1214/09-LNMS5710

Primary: 62G20, 62G30
Secondary: 60F05

Rights: Copyright © 2009, Institute of Mathematical Statistics


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