Abstract Details
Activity Number:
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691
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Type:
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Contributed
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Date/Time:
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Thursday, August 8, 2013 : 10:30 AM to 12:20 PM
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Sponsor:
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IMS
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Abstract - #307908 |
Title:
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The Limit Distribution of the Supremum-Error of Grenander-Type Estimators
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Author(s):
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Hendrik Lopuhaa*+ and Cecile Durot and Vladimir Kulikov
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Companies:
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Delft University of Technology and Univeristy of Nanterre and ASR Nederland
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Keywords:
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Supremum distance ;
Extremal limit theorem ;
Least concave majorant ;
Monotone density ;
Monotone regression ;
Monotone failure rate
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Abstract:
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Let $f$ be a non-increasing function defined on $[0,1]$. Under standard regularity conditions, we derive the asymptotic distribution of the supremum distance between $f$ and its isotonic estimator on any interval $(\alpha_n, 1 - \alpha_n] \subset [0,1]$, where $\alpha_n$ tends to zero at a suitable rate. The rate of convergence of the supremum distance is found to be of order $(\log n /n)^{1/3}$ and the limiting distribution turns out to be Gumbel with a parameter depending on a functional of $f$ and $f'$. The results are obtained in a general framework, which includes the Grenander estimator of a decreasing density, the least squares estimator of a monotone regression curve or an isotonic estimator of a decreasing hazard of right-censored observations.
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Authors who are presenting talks have a * after their name.
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