An equality test across nonparametric regressions

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Breaking the curse of dimensionality in nonparametric testing (2008, background): “When testing for the significance of some regressors Z in a nonparametric regression on X = (X1, Z), U(θ) = Y − E (Y |X1), see Fan and Li (1996), Lavergne and Vuong (2000), Aı̈t-Sahalia, Bickel and Stoker (2001), Delgado and Gonzalez-Manteiga (2001), Lavergne (2001).”
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.”
Testing the Significance of Categorical Predictor Variables in Nonparametric Regression Models (2006, methodology): “We also consider the parametric Chow test reported in Lavergne (2001) which serves as a benchmark upper bound on performance.”