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April 2006 The behavior of the NPMLE of a decreasing density near the boundaries of the support
Vladimir N. Kulikov, Hendrik P. Lopuhaä
Ann. Statist. 34(2): 742-768 (April 2006). DOI: 10.1214/009053606000000100


We investigate the behavior of the nonparametric maximum likelihood estimator n for a decreasing density f near the boundaries of the support of f. We establish the limiting distribution of n(nα), where we need to distinguish between different values of 0<α<1. Similar results are obtained for the upper endpoint of the support, in the case it is finite. This yields consistent estimators for the values of f at the boundaries of the support. The limit distribution of these estimators is established and their performance is compared with the penalized maximum likelihood estimator.


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Vladimir N. Kulikov. Hendrik P. Lopuhaä. "The behavior of the NPMLE of a decreasing density near the boundaries of the support." Ann. Statist. 34 (2) 742 - 768, April 2006.


Published: April 2006
First available in Project Euclid: 27 June 2006

zbMATH: 1092.62044
MathSciNet: MR2283391
Digital Object Identifier: 10.1214/009053606000000100

Primary: 62E20 , 62G07
Secondary: 62G20

Keywords: asymptotic distribution , estimating a monotone density at zero , Grenander estimator , isotonic estimation

Rights: Copyright © 2006 Institute of Mathematical Statistics

Vol.34 • No. 2 • April 2006
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