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Activity Number:
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508
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Type:
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Contributed
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Date/Time:
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Thursday, August 2, 2007 : 8:30 AM to 10:20 AM
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Sponsor:
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IMS
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| Abstract - #308883 |
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Title:
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Uniform Central Limit Theorems for Density Estimators
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Author(s):
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Richard Nickl*+
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Companies:
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University of Connecticut
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Address:
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Department of Mathematics, Storrs, CT, 06269,
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Keywords:
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density estimation ; empirical processes ; uniform central limit theorems ; nonparametric maximum likelihood
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Abstract:
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Let p_n be some nonparametric density estimator based on n independent observations each distributed according to the law P. Define the stochastic process $f\mapsto \sqrt{n}\int f(p_n(x)dx-dP(x)$ where f ranges over some class of functions F. We say that p_n satisfies a uniform central limit theorem if the process defined above converges in law in the Banach space of bounded functions on F to a mean zero Gaussian process. We discuss recent results of this kind for classical density estimators such as trigonometric series, (sieved) maximum likelihood and kernel density estimators. (Part of this is joint work with Evarist Gine).
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