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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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    2. Miller, Forrest R. & Neill, James W., 2016. "Lack of fit tests for linear regression models with many predictor variables using minimal weighted maximal matchings," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 14-26.
    3. Li, Lingzhu & Chiu, Sung Nok & Zhu, Lixing, 2019. "Model checking for regressions: An approach bridging between local smoothing and global smoothing methods," Computational Statistics & Data Analysis, Elsevier, vol. 138(C), pages 64-82.
    4. Liu, Ran & Zhu, Lixing, 2023. "Specification testing for ordinary differential equation models with fixed design and applications to COVID-19 epidemic models," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    5. Chuanlong Xie & Lixing Zhu, 2018. "A minimum projected-distance test for parametric single-index Berkson models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 700-715, September.
    6. Jun Lu & Lu Lin, 2020. "Model-free conditional screening via conditional distance correlation," Statistical Papers, Springer, vol. 61(1), pages 225-244, February.
    7. Xie, Chuanlong & Zhu, Lixing, 2019. "A goodness-of-fit test for variable-adjusted models," Computational Statistics & Data Analysis, Elsevier, vol. 138(C), pages 27-48.
    8. Junmin Liu & Deli Zhu & Luoyao Yu & Xuehu Zhu, 2023. "Specification testing of partially linear single-index models: a groupwise dimension reduction-based adaptive-to-model approach," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 232-262, March.
    9. Maistre, Samuel & Lavergne, Pascal & Patilea, Valentin, 2014. "Powerful nonparametric checks for quantile regression," TSE Working Papers 14-501, Toulouse School of Economics (TSE).
    10. Cuizhen Niu & Lixing Zhu, 2018. "A robust adaptive-to-model enhancement test for parametric single-index models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(5), pages 1013-1045, October.

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    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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