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

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Abstract
We develop a novel approach to build checks of parametric regression models when many regressors are present, based on a class of rich enough 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 one regressor only, whatever the number of regressors. This test can be viewed as a smooth version of the integrated conditional moment (ICM) test of Bierens. Qualitative information can be easily incorporated in the procedure to enhance power. Our test is little sensitive to the smoothing parameter and performs better than several known lack-of-fit tests in multidimensional settings, as illustrated by extensive simulations and an application to a cross-country growth regression.

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  • Pascal Lavergne & Valentin Patilea, 2008. "One for All and All for One:Regression Checks With Many Regressors," Discussion Papers dp08-06, Department of Economics, Simon Fraser University.
    • Handle: RePEc:sfu:sfudps:dp08-06
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    References listed on IDEAS

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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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    More about this item

    Keywords

    Dimensionality; Hypothesis testing; Nonparametric methods;
    All these keywords.

    JEL classification:

    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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