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A CONSISTENT DIAGNOSTIC TEST FOR REGRESSION MODELS USINGPROJECTIONS

Published online by Cambridge University Press:  03 November 2006

J. Carlos Escanciano
J. Carlos Escanciano
Affiliation:
Universidad de Navarra
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Abstract

This paper proposes a consistent test for the goodness-of-fit ofparametric regression models that overcomes two important problemsof the existing tests, namely, the poor empirical power and sizeperformance of the tests due to the curse of dimensionality and thesubjective choice of parameters such as bandwidths, kernels, andintegrating measures. We overcome these problems by using a residualmarked empirical process based on projections (RMPP). We study theasymptotic null distribution of the test statistic, and we show thatour test is able to detect local alternatives converging to the nullat the parametric rate. It turns out that the asymptotic nulldistribution of the test statistic depends on the data generatingprocess, and so a bootstrap procedure is considered. Our bootstraptest is robust to higher order dependence, in particular toconditional heteroskedasticity. For completeness, we propose a newminimum distance estimator constructed through the same RMPP as inthe testing procedure. Therefore, the new estimator inherits all thegood properties of the new test. We establish the consistency andasymptotic normality of the new minimum distance estimator. Finally,we present some Monte Carlo evidence that our testing procedure canplay a valuable role in econometric regression modeling.The author thanks Carlos Velasco andMiguel A. Delgado for useful comments. The paper has alsobenefited from the comments of two referees and the co-editor.This research was funded by the Spanish Ministry of Educationand Science reference number SEJ2004-04583/ECON and by theUniversidad de Navarra reference number 16037001.

Information

Type
Research Article
Information
Econometric Theory , Volume 22 , Issue 6 , December 2006 , pp. 1030 - 1051
Copyright
© 2006 Cambridge University Press

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