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December, 1993 Comparing Nonparametric Versus Parametric Regression Fits
W. Hardle, E. Mammen
Ann. Statist. 21(4): 1926-1947 (December, 1993). DOI: 10.1214/aos/1176349403


In general, there will be visible differences between a parametric and a nonparametric curve estimate. It is therefore quite natural to compare these in order to decide whether the parametric model could be justified. An asymptotic quantification is the distribution of the integrated squared difference between these curves. We show that the standard way of bootstrapping this statistic fails. We use and analyse a different form of bootstrapping for this task. We call this method the wild bootstrap and apply it to fitting Engel curves in expenditure data analysis.


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W. Hardle. E. Mammen. "Comparing Nonparametric Versus Parametric Regression Fits." Ann. Statist. 21 (4) 1926 - 1947, December, 1993.


Published: December, 1993
First available in Project Euclid: 12 April 2007

zbMATH: 0795.62036
MathSciNet: MR1245774
Digital Object Identifier: 10.1214/aos/1176349403

Primary: 62G07
Secondary: 62G09

Keywords: bootstrap , Goodness-of-fit test , kernel estimate , wild bootstrap

Rights: Copyright © 1993 Institute of Mathematical Statistics


Vol.21 • No. 4 • December, 1993
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