Institute of Mathematical Statistics Lecture Notes - Monograph Series

On the Estimation of Symmetric Distributions under Peakedness Order Constraints

Javier Rojo and José Batún-Cutz

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Abstract

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.

Chapter information

Source
Javier Rojo, ed., Optimality: The Third Erich L. Lehmann Symposium (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2009), 147-172

Dates
First available in Project Euclid: 3 August 2009

Permanent link to this document
https://projecteuclid.org/euclid.lnms/1249305328

Digital Object Identifier
doi:10.1214/09-LNMS5710

Zentralblatt MATH identifier
1271.62076

Subjects
Primary: 62G30: Order statistics; empirical distribution functions 62G20: Asymptotic properties
Secondary: 60F05: Central limit and other weak theorems

Keywords
partial orders nonparametric statistics stochastic order empirical process weak convergence

Rights
Copyright © 2009, Institute of Mathematical Statistics

Citation

Rojo, Javier. On the Estimation of Symmetric Distributions under Peakedness Order Constraints. Optimality, 147--172, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2009. doi:10.1214/09-LNMS5710. https://projecteuclid.org/euclid.lnms/1249305328


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