A CONSISTENT NONPARAMETRIC TEST OF PARAMETRIC REGRESSION MODELS UNDER CONDITIONAL QUANTILE RESTRICTIONS

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Abstract
This paper proposes a nonparametric, kernel-based test of parametric quantile regression models. The test statistic has a limiting standard normal distribution if the parametric quantile model is correctly specified and diverges to infinity for any misspecification of the parametric model. Thus the test is consistent against any fixed alternative. The test also has asymptotic power 1 against local alternatives converging to the null at proper rates. A simulation study is provided to evaluate the finite-sample performance of the test.