Lavergne, Pascal and Patilea, Valentin (2011): 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 sufficiently rich semiparametric alternatives, namely singleindex 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 into the procedure to enhance power. In an extensive comparative simulation study, we find that our test is little sensitive to the smoothing parameter and performs well in multidimensional settings. We then apply it to a crosscountry growth regression model.
Item Type:  MPRA Paper 

Original Title:  One for all and all for one: regression checks with many regressors 
Language:  English 
Keywords:  Dimensionality, Hypothesis testing, Nonparametric methods 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C14  Semiparametric and Nonparametric Methods: General C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C12  Hypothesis Testing: General 
Item ID:  35779 
Depositing User:  Pascal Lavergne 
Date Deposited:  06. Jan 2012 23:08 
Last Modified:  18. Mar 2015 10:11 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/35779 