Data-Driven Rate-Optimal Specification Testing in Regression Models

We propose new data-driven smooth tests for a parametric regression function. The smoothing parameter is selected through a new criterion that favors a large smoothing parameter under the null hypothesis. The resulting test is adaptive rate-optimal and consistent against Pitman local alternatives ap...

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Bibliographic Details
Published in:The Annals of statistics 2005-04, Vol.33 (2), p.840-870
Main Authors: Guerre, Emmanuel, Lavergne, Pascal
Format: Article
Language:English
Subjects:
62G08
62G10
Critical values
Data smoothing
Estimators
Hypothesis testing
Linear regression
nonparametric adaptive tests
Null hypothesis
Parametric models
Polynomials
Regression analysis
Regression Methodology
selection methods
Statistical theories
Statistical variance
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Description
Summary:We propose new data-driven smooth tests for a parametric regression function. The smoothing parameter is selected through a new criterion that favors a large smoothing parameter under the null hypothesis. The resulting test is adaptive rate-optimal and consistent against Pitman local alternatives approaching the parametric model at a rate arbitrarily close to 1/√n. Asymptotic critical values come from the standard normal distribution and the bootstrap can be used in small samples. A general formalization allows one to consider a large class of linear smoothing methods, which can be tailored for detection of additive alternatives.
ISSN:0090-5364
2168-8966
DOI:10.1214/009053604000001200