A NONPARAMETRIC BOOTSTRAP TEST OF CONDITIONAL DISTRIBUTIONS

This paper proposes a bootstrap test for the correct specification of parametric conditional distributions. It extends Zheng's test (Zheng, 2000, Econometric Theory 16, 667–691) to allow for discrete dependent variables and for mixed discrete and continuous conditional variables. We establish the asymptotic null distribution of the test statistic with data-driven stochastic smoothing parameters. By smoothing both the discrete and continuous variables via the method of cross-validation, our test has the advantage of automatically removing irrelevant variables from the estimate of the conditional density function and, as a consequence, enjoys substantial power gains in finite samples, as confirmed by our simulation results. The simulation results also reveal that the bootstrap test successfully overcomes the size distortion problem associated with Zheng's test.We are grateful for the insightful comments from three referees and a co-editor that greatly improved the paper. Li's research is partially supported by the Private Enterprise Research Center, Texas A&M University. Fan is grateful to the National Science Foundation for research support.

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