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October 1998 The silhouette, concentration functions and ML-density estimation under order restrictions
Wolfgang Polonik
Ann. Statist. 26(5): 1857-1877 (October 1998). DOI: 10.1214/aos/1024691360

Abstract

Based on empirical Lévy-type concentration functions, a new graphical representation of the ML-density estimator under order restrictions is given. This representation generalizes the well-known representation of the Grenander estimator of a monotone density as the slope of the least concave majorant of the empirical distribution function to higher dimensions and arbitrary order restrictions. From the given representation it follows that a density estimator called silhouette, which arises naturally out of the excess mass approach, is the ML-density estimator under order restrictions. This fact provides a new point of view to ML-density estimation from which one gains additional insight to this problem, as demonstrated in the present paper.

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Wolfgang Polonik. "The silhouette, concentration functions and ML-density estimation under order restrictions." Ann. Statist. 26 (5) 1857 - 1877, October 1998. https://doi.org/10.1214/aos/1024691360

Information

Published: October 1998
First available in Project Euclid: 21 June 2002

zbMATH: 1073.62523
MathSciNet: MR1673281
Digital Object Identifier: 10.1214/aos/1024691360

Subjects:
Primary: 62G07
Secondary: 62A10, 62G20, 62G30

Rights: Copyright © 1998 Institute of Mathematical Statistics

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Vol.26 • No. 5 • October 1998
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