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One for All and All for One: Regression Checks With Many Regressors

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  • Pascal Lavergne
  • Valentin Patilea

Abstract

We develop a novel approach to building checks of parametric regression models when many regressors are present, based on a class of sufficiently rich semiparametric alternatives, namely single-index models. We propose an omnibus test based on the kernel method that performs against a sequence of directional nonparametric alternatives as if there was only one regressor whatever the number of regressors. This test can be viewed as a smooth version of the integrated conditional moment test of Bierens. Qualitative information can be easily incorporated into the procedure to enhance power. In an extensive comparative simulation study, we find that our test is not very sensitive to the smoothing parameter and performs well in multidimensional settings. We apply this test to a cross-country growth regression model.

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  • Pascal Lavergne & Valentin Patilea, 2011. "One for All and All for One: Regression Checks With Many Regressors," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(1), pages 41-52, January.
  • Handle: RePEc:taf:jnlbes:v:30:y:2011:i:1:p:41-52
    DOI: 10.1198/jbes.2011.07152
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    Cited by:

    1. Maistre, Samuel & Lavergne, Pascal & Patilea, Valentin, 2014. "Powerful nonparametric checks for quantile regression," TSE Working Papers 14-501, Toulouse School of Economics (TSE).

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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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