A Powerful Chi-Square Specification Test with Support Vectors

Abstract: Specification tests, such as Integrated Conditional Moment (ICM) and Kernel Conditional Moment (KCM) tests, are crucial for model validation but often lack power in finite samples. This paper proposes a novel framework to enhance specification test performance using Support Vector Machines (SVMs) for direction learning. We introduce two alternative SVM-based approaches: one maximizes the discrepancy between nonparametric and parametric classes, while the other maximizes the separation between residuals and the origin. Both approaches lead to a $t$-type test statistic that converges to a standard chi-square distribution under the null hypothesis. Our method is computationally efficient and capable of detecting any arbitrary alternative. Simulation studies demonstrate its superior performance compared to existing methods, particularly in large-dimensional settings.