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A General Nonparametric Test for Misspecification

Ralph Bradley and Robert McClelland


We establish a new consist, uniformly most powerful test for misspecification. Unlike most previous work, we use a constrained cross-validation scheme for smoothing parameter selection, so that the test does not require arbitrary parameter selections. We address the degeneracy issue through a bootstrap procedure that also allows us to establish the asymptotic distribution of our test statistic. By allowing the use of higher-order kernels without the calculation of higher order derivatives, our test should be simpler to calculate and more powerful than similar tests. Finally, we show that out test can be applied to discrete as well as continuous regressors.