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On approximations to the bias of the nadaraya-watson regression estimator 

Author: Klaus Ziegler a
Affiliation:   a Mathematical Institute, University of Munich, Munich, Germany
DOI: 10.1080/10485250108832866
Publication Frequency: 8 issues per year
Published in: journal Journal of Nonparametric Statistics, Volume 13, Issue 4 2001 , pages 583 - 589
Formats available: PDF (English)
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Abstract

The Nadaraya Watson regression curve estimator is given as a ratio m = f/g. Under very mild assumptions (in particular not including any continuity of the regression function or design density), the uniform asymptotic deviation of the expectation Em from the ratio Er/Eg (a quantity usually appearing in inspections of the asymptotic properties of m) is investigated. Our approach covers several types of data-dependent bandwidths and remains valid for classes of regression functions.
Keywords: Nonparametric regression; Random design; Kernel smoothing; Rates of uniform convergence
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