2012
DOI: 10.1198/jbes.2011.07152
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One for All and All for One: Regression Checks With Many Regressors

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 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. Qualit… Show more

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Cited by 25 publications
(15 citation statements)
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“…With some regularity conditions, the test statistic multiplying nh p/2 goes to its weak limit under the null where h → 0 as n → ∞. Lavergne and Patilea (2012)'s test is an integrated Zheng (1996)'s test over all projection directions α ∈ S p . It has the formula as…”
Section: Test Constructionmentioning
confidence: 99%
See 4 more Smart Citations
“…With some regularity conditions, the test statistic multiplying nh p/2 goes to its weak limit under the null where h → 0 as n → ∞. Lavergne and Patilea (2012)'s test is an integrated Zheng (1996)'s test over all projection directions α ∈ S p . It has the formula as…”
Section: Test Constructionmentioning
confidence: 99%
“…Also, the integral does not have a closed form and then the computation is an issue when the dimension p is high. Lavergne and Patilea (2012) used a Monte Carlo approximation for this integral. The computation is time-consuming in high-dimensional scenarios.…”
Section: Test Constructionmentioning
confidence: 99%
See 3 more Smart Citations