Bootstrapping the Grenander estimator
Michael R. Kosorok
Abstract
The goal of this paper is to study the bootstrap for the Grenander estimator. The first result is a proof of the inconsistency of the nonparametric bootstrap for the Grenander estimator at a given point. The second result is the development and verification of a bootstrap for the L1 confidence band for the Grenander estimator. As part of this work, kernel estimators are studied as alternatives to the Grenander estimator. We show that when the second derivative of the true density is assumed to be uniformly bounded, there exist kernel estimators with faster convergence rates than the Grenander estimator. We study the implications of this in developing L1 and uniform confidence bands and discuss some open questions.
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Primary Subjects: 62G09, 62G07
Secondary Subjects: 60F05, 60G15
Keywords: Chernoff’s distribution; confidence bands; kernel estimators; L_1 error; Monte Carlo methods; pointwise error; uniform error
Full-text: Open access
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Permanent link to this document: http://projecteuclid.org/euclid.imsc/1207058280
Digital Object Identifier: doi:10.1214/193940307000000202
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