Specification tests in nonparametric regression

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Testing for the equality of k regression curves (2007, methodology): “See Freedman (1981) for the bootstrap of the residuals and, e.”
On Testing Independence and Goodness-of-fit in Linear Models (2013, methodology): “In the nonparametric setup, [ EVK08b] and [EVK08a] propose tests for independence but only for univariate covariates.”