The Annals of Statistics

Comparing Nonparametric Versus Parametric Regression Fits

W. Hardle and E. Mammen

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 21, Number 4 (1993), 1926-1947.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349403

Digital Object Identifier
doi:10.1214/aos/1176349403

Mathematical Reviews number (MathSciNet)
MR1245774

Zentralblatt MATH identifier
0795.62036

JSTOR
links.jstor.org

Subjects
Primary: 62G07: Density estimation
Secondary: 62G09: Resampling methods

Keywords
Kernel estimate bootstrap wild bootstrap goodness-of-fit test

Citation

Hardle, W.; Mammen, E. Comparing Nonparametric Versus Parametric Regression Fits. Ann. Statist. 21 (1993), no. 4, 1926--1947. doi:10.1214/aos/1176349403. https://projecteuclid.org/euclid.aos/1176349403


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