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Activity Number:
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121
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Type:
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Invited
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Date/Time:
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Monday, July 30, 2007 : 10:30 AM to 12:20 PM
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Sponsor:
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IMS
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| Abstract - #307849 |
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Title:
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A Mean-Matching, Variance-Stabilizing Transform Approach to Nonparametric Regression in Exponential Families
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Author(s):
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Tony Cai*+
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Companies:
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University of Pennsylvania
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Address:
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The Wharton School, 3730 Walnut Street, Philadelphia, PA, 19104-6340,
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Keywords:
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adaptive estimation ; block thresholding ; exponential families ; nonparametric regression ; variance stabilizing transform ; wavelets
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Abstract:
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Most of the nonparametric regression theory is developed for the case of additive Gaussian noise. In such a setting many smoothing techniques including wavelet thresholding methods have been developed and shown to be highly adaptive. In this talk we consider nonparametric regression in exponential families which include, for example, Poisson regression, binomial regression, and Gamma regression. We take the approach of using a mean-matching variance stabilizing transform to convert the problem into a standard homoskedastic Gaussian regression problem. A wavelet block thresholding method is then used to construct the final estimator of the regression function. The procedure is easily implementable. Both numerical and theoretical properties of the estimator are investigated. In particular the estimators are shown to be adaptively rate-optimal over a range of Besov Spaces.
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- The address information is for the authors that have a + after their name.
- Authors who are presenting talks have a * after their name.
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