Abstract Details
Activity Number:
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548
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Type:
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Contributed
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Date/Time:
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Wednesday, August 7, 2013 : 10:30 AM to 12:20 PM
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Sponsor:
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Section on Nonparametric Statistics
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Abstract - #310472 |
Title:
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Adaptive Density Estimation Based on Real and Artificial Data
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Author(s):
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Tina Felber*+ and Michael Kohler and Adam Krzyzak
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Companies:
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TU Darmstadt and TU Darmstadt and Concordia University
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Keywords:
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Density estimation ;
$L_1$-error ;
nonparametric regression ;
consistency ;
rate of convergence
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Abstract:
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Let X, X1, X2,... be independent and identically distributed Rd-valued random variables and let m : Rd ! R be a measurable function such that a density f of Y = m(X) exists. The problem of estimating f based on a sample of the ditribution of (X; Y ) and on additional independent observations of X is considered. Two kernel density estimates are compared: the standard kernel density estimate based on the y-values of the sample of (X; Y ), and a kernel density estimate based on artificially generated y-values corresponding to the additional observations of X. It is shown that under suitable smoothness assumptions on f and m the rate of convergence of the L1-error of the latter estimate is better than the standard kernel density estimate. Furthermore, a density estimate defined as convex combination of these two estimates is considered and a datadriven choice of its parameters (bandwidths and weight of the convex combination) is proposed and analyzed.
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