Abstract: For a nonparametric regression model with a fixed design, we consider the model specification test based on a kernel. We find that a bimodal kernel is useful for the model specification test with a correlated error, whereas a conventional unimodal kernel is useful only for an iid error. Another finding is that the model specification test suffers from a convergence rate change depending on whether the errors are correlated or not. These results are verified by deriving an asymptotic null distribution and asymptotic (local) power, and by performing a simulation. The validity of the bimodal kernel for testing is demonstrated with the “drum roller” data (see Laslett(1994) and Altman (1994)).

Key words and phrases: bimodal kernel, convergence rate change, correlated error, nonparametric specification test.