RKHS-based specification for the regression function

M. Vidal García, I. Van Keilegom, R. Crujeiras, W. González-Manteiga

A new goodness-of-fit test for the regression function is proposed using the RKHS methodology (Machine Learning). The construction of the test statistic is explained highlighting the role of the underlying empirical process. Then, its asymptotic distribution is studied under the null, fixed and local alternatives. Regarding its implementation, the theoretical validity of suitable resampling techniques is established, and its performance assessed via simulations. The effect of the tuning parameter will be discussed along with several criteria in the literature to adress this issue. Finally, the application of this methodology will be illustrated using ecology data.

This work is part of the R&D project PID2020-116587GBI00
granted by MICIU/AEI/10.13039/501100011033

Keywords: maximum mean discrepancy; RKHS; scale-location model; specification test; regression.

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