2024 European Winter Meeting, Palma de Majorca, Spain: December, 2024
Testing Regression Models with Kernel Fisher Discriminant Analysis
Yuhao Li; Xiaojun Song
This paper introduces a novel approach to enhancing the goodness-of-fit test for regression models using kernel Fisher discriminant analysis. The proposed method incorporates the covariance structure of integrated regression functions into the test statistics. Unlike existing test statistics, the new approach uniformly weights the components associated with the leading eigenvalues of the covariance operator and downweights the remaining ones. This allows for greater testing power by focusing on a user-tunable number of components. Additionally, under certain assumptions regarding the convergence speed of the regularization term, the test statistic can be made pivotal.
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