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Activity Number:
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261
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Type:
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Invited
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Date/Time:
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Tuesday, July 31, 2007 : 10:30 AM to 12:20 PM
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Sponsor:
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IMS
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| Abstract - #307894 |
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Title:
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Adaptive Nonparametric Density Estimation via the Root-Unroot Transform and Wavelet Block Threshholding
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Author(s):
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Lawrence D. Brown*+
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Companies:
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University of Pennsylvania
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Address:
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Wharton School, Department of Statistics, Philadelphia, PA, 19104,
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Keywords:
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density estimation ; nonparametric regression ; wavelets ; Poisson regression ; root-unroot transform ; adaptive estimation
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Abstract:
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Nonparametric density estimation has traditionally been treated separately from nonparametric regression. Here, we propose an approach that first transforms a density estimation problem into a nonparametric regression problem. The algorithm for this involves suitably binning the observations and then transforming the binned data counts via a carefully chosen square-root transformation. A wavelet block-threshholding rule is then used for the regression problem, and produces an estimated nonparametric regression function. Finally an adjusted un-root transform is applied to yield the final nonparametric density estimator. The procedure is easy to implement. It enjoys a high degree of asymptotic adaptivity and is shown in numerical examples to perform well for standard density estimation settings.
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