Abstract Details
Activity Number:
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15
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Type:
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Topic Contributed
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Date/Time:
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Sunday, August 4, 2013 : 2:00 PM to 3:50 PM
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Sponsor:
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Section on Nonparametric Statistics
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Abstract - #307674 |
Title:
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The Grenander Estimator Under Model Misspecification
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Author(s):
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Hanna Jankowski*+ and Jon Wellner
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Companies:
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York University and University of Washington
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Keywords:
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nonparametric ;
misspecification ;
Grenander ;
maximum likelihood ;
shape-constraints ;
convergence rates
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Abstract:
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Under the assumption that the true density is decreasing, it is well known that the Grenander estimator converges at rate n^{-1/3} if the true density is curved and at rate n^{-1/2} if the density is flat. In the case that the true density is misspecified, the results of Patilea (2001) tell us that the global convergence rate is of order n^{-1/3}. We show that the local convergence rate is n^{-1/2} at a point where the density is misspecified. This is not in contradiction with the results of Patilea: the global convergence rate simply comes from locally curved well-specified regions. Furthermore, we study global convergence under misspecification by considering linear functionals. The rate of convergence is n^{-1/2} and we show that the limit is made up of two independent terms: a mean-zero Gaussian term and a second term (with non-zero mean) which is present only if the density has well-specified locally flat regions.
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Authors who are presenting talks have a * after their name.
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