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2009 Estimation of a discrete monotone distribution
Hanna K. Jankowski, Jon A. Wellner
Electron. J. Statist. 3: 1567-1605 (2009). DOI: 10.1214/09-EJS526

Abstract

We study and compare three estimators of a discrete monotone distribution: (a) the (raw) empirical estimator; (b) the “method of rearrangements” estimator; and (c) the maximum likelihood estimator. We show that the maximum likelihood estimator strictly dominates both the rearrangement and empirical estimators in cases when the distribution has intervals of constancy. For example, when the distribution is uniform on {0,,y}, the asymptotic risk of the method of rearrangements estimator (in squared 2 norm) is y/(y+1), while the asymptotic risk of the MLE is of order (logy)/(y+1). For strictly decreasing distributions, the estimators are asymptotically equivalent.

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Hanna K. Jankowski. Jon A. Wellner. "Estimation of a discrete monotone distribution." Electron. J. Statist. 3 1567 - 1605, 2009. https://doi.org/10.1214/09-EJS526

Information

Published: 2009
First available in Project Euclid: 7 January 2010

zbMATH: 1326.62038
MathSciNet: MR2578839
Digital Object Identifier: 10.1214/09-EJS526

Subjects:
Primary: 62E20 , 62F12
Secondary: 62C15 , 62F20 , 62G07 , 62G30

Keywords: Grenander estimator , limit distributions , maximum likelihood , monotone mass function , nonparametric estimation , rate of convergence , rearrangement , shape restriction

Rights: Copyright © 2009 The Institute of Mathematical Statistics and the Bernoulli Society

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