Goodness-of-fit tests for kernel regression with an application to option implied volatilities

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Testing and imposing Slutsky symmetry in nonparametric demand systems (2009, methodology): “Then the following functional expansion holds (analogous to Lemma A.1 in Aït-Sahalia et al., 2001).”
A consistent model specification test with mixed discrete and continuous data (2007, unknown): “See Andrews (1997), Bierens and Ploberger (1997), Donald (1997), and Ait-Sahalia, Bickel and Stoker (2001) and the references therein for recent developments in consistent model specification testing.”
A NONPARAMETRIC HELLINGER METRIC TEST FOR CONDITIONAL INDEPENDENCE (2008, background): “The proof relies on a functional expansion of Γ(., F ), as in Ait-Sahalia et al. (2001), and some preliminary U -statistic results in Tenreiro (1997).”
Nonparametric checks for single-index models (2005, methodology): “The comparison is among our maximin test, the omnibus test T̃n, Fan and Li [14] (FLtest) and Aït-Sahalia, Bickel and Stoker [1] (ABS-test).”