Abstract: Consider the nonparametric regression model , where the function is smooth, but unknown. We construct tests for the independence of and , based on independent copies of . The testing procedures are based on differences of neighboring 's. We establish asymptotic results for the proposed tests statistics, investigate their finite sample properties through a simulation study and present an econometric application to household data. The proofs are based on delicate empirical process theory.
Key words and phrases: Empirical process, model diagnostics, nonparametric regression, test for independence, weak convergence.