A kernel-based goodness-of-fit test for regression models
Over the last decade there has been considerable progress in the development of statistical methods relying on the kernel approach, which originates in the field of Machine Learning.
This work proposes a kernel-based specification test for the regression function in the context of scale-location models. Following previous literature, it relies on expressing the original contrast as a contrast over the distribution of the residuals. The novelty is to use the maximum mean discrepancy, a notion arising when embedding the observations into a Reproducing Kernel Hilbert Space. A review on the theoretical framework is provided before introducing the new proposal along with its theoretical properties.
Finally, issues regarding implementation are addressed. As is often the case, implementation based on the asymptotic distribution leads to poor computational results, so resampling methods are preferred. Its performance is assessed and compared to other alternatives via simulations.
Palabras clave: maximum mean discrepancy RKHS scale-location model specification test