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Simple transformation techniques for improved nonparametric regression

Park, B. U.; Kim, W. C.; Ruppert, D.; Jones, M. C.; Signorini, D. F. and Kohn, R. (1997). Simple transformation techniques for improved nonparametric regression. Scandinavian Journal of Statistics, 24(2) pp. 145–163.

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We propose and investigate two new methods for achieving less bias in non- parametric regression. We show that the new methods have bias of order h4, where h is a smoothing parameter, in contrast to the basic kernel estimator’s order h2. The methods are conceptually very simple. At the first stage, perform an ordinary non-parametric regression on {xi, Yi} to obtain m^(xi) (we use local linear fitting). In the first method, at the second stage, repeat the non-parametric regression but on the transformed dataset {m^(xi, Yi)}, taking the estimator at x to be this second stage estimator at m^(x). In the second, and more appealing, method, again perform non-parametric regression on {m^(xi, Yi)}, but this time make the kernel weights depend on the original x scale rather than using the m^(x) scale. We concentrate more of our effort in this paper on the latter because of its advantages over the former. Our emphasis is largely theoretical, but we also show that the latter method has practical potential through some simulated examples.

Item Type: Journal Item
Copyright Holders: 1997 Scandinavian Journal of Statistics
ISSN: 0303-6898
Keywords: kernel smoothing; local linear regression; local polynomial regression; reduced bias
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 24109
Depositing User: Sarah Frain
Date Deposited: 11 May 2011 10:56
Last Modified: 07 Dec 2018 09:42
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