Open Access
2008 Empirical likelihood based testing for regression
Ingrid Van Keilegom, César Sánchez Sellero, Wenceslao González Manteiga
Electron. J. Statist. 2: 581-604 (2008). DOI: 10.1214/07-EJS152


Consider a random vector (X,Y) and let m(x)=E(Y|X=x). We are interested in testing $H_{0}:m\in {\cal M}_{\Theta,{\cal G}}=\{\gamma(\cdot,\theta,g):\theta \in \Theta,g\in {\cal G}\}$ for some known function γ, some compact set $\Theta \subset I\!\!R^{p}$ and some function set ${\cal G}$ of real valued functions. Specific examples of this general hypothesis include testing for a parametric regression model, a generalized linear model, a partial linear model, a single index model, but also the selection of explanatory variables can be considered as a special case of this hypothesis.

To test this null hypothesis, we make use of the so-called marked empirical process introduced by [4] and studied by [16] for the particular case of parametric regression, in combination with the modern technique of empirical likelihood theory in order to obtain a powerful testing procedure. The asymptotic validity of the proposed test is established, and its finite sample performance is compared with other existing tests by means of a simulation study.


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Ingrid Van Keilegom. César Sánchez Sellero. Wenceslao González Manteiga. "Empirical likelihood based testing for regression." Electron. J. Statist. 2 581 - 604, 2008.


Published: 2008
First available in Project Euclid: 16 July 2008

zbMATH: 1320.62034
MathSciNet: MR2426103
Digital Object Identifier: 10.1214/07-EJS152

Primary: 62E20
Secondary: 62F03 , 62F05 , 62F40 , 62G08 , 62G10

Keywords: Marked empirical process , model check for regression , Nonlinear regression , Partial linear model , residuals

Rights: Copyright © 2008 The Institute of Mathematical Statistics and the Bernoulli Society

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