Department of Mathematics
Indian Institute of Science
Bangalore 560 012
SEMINAR
Speaker |
: |
Dr. Moulinath Banerjee |
Affiliation | : | University of Michigan |
Subject Area |
: |
Mathematics
|
Venue |
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Lecture Hall - I, Dept of Mathematics
|
Time |
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4.00 pm
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Date |
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August 13,2008 (Wednesday) |
Title |
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Inconsistency of the Bootstrap in Problems Exhibiting Cube Root Asymptotics |
Abstract | : |
We investigate the
(in)-consistency of different bootstrap methods for constructing confidence
intervals in the class of estimators that converge at rate $n^{1\over 3}$.
The Grenander estimator, the nonparametric maximum likelihood estimator of
an unknown non-increasing density function $f$ on $[0,\infty)$, is a
prototypical example. We focus on this example and explore different
approaches to constructing bootstrap confidence intervals for $f(t_0)$,
where $t_0 \in (0,\infty)$ is an interior point. We find that the bootstrap
estimate, when generating bootstrap samples from the empirical distribution
function or its least concave majorant, does not have any weak limit in
probability. Bootstrapping from a smoothed version of the least concave
majorant, however, leads to strongly This is joint work with
Bodhisattva Sen and Michael Woodroofe.
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