Breaking the curse of dimensionality in nonparametric testing

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An updated review of Goodness-of-Fit tests for regression models (2013, methodology): “For the tests based on smoothing methods, corresponding to process αn, the works by Lavergne and Patilea (2008) and Xia (2009) should be noticed.”
A Goodness-of-Fit Test for the Functional Linear Model with Scalar Response (2012, methodology): “More recently, Patilea et al. (2012) provide a projection–based test for functional covariate e ffect in a functional regression model with scalar response. In their paper, the authors adapt the tests of Zheng (1996) and Lavergne and Patilea (2008), based on smoothing techniques, to the context of f”