Testing for Neglected Nonlinearity Using Extreme Learning Machines (published in: International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 21, Suppl. 2 (2013), 117--129.)

In this study, we introduce statistics for testing neglected nonlinearity using the extreme leaning machines introduced by Huang, Zhu, and Siew (2006, Neurocomputing) and call them ELMNN tests. The ELMNN tests are very convenient and can be widely applied because they are obtained as byproducts of estimating linear models, and they can serve as quick diagnostic test statistics complementing the computational burdens of other tests. For the proposed test statistics, we provide a set of regularity conditions under which they asymptotically follow a chi-squared distribution under the null and are consistent under the alternative. We conduct Monte Carlo experiments and examine how they behave when the sample size is finite. Our experiment shows that the tests exhibit the properties desired by the theory of this paper.