## A consistent model specification test with mixed discrete and continuous data.(English)Zbl 1247.62126

Summary: In this paper we propose a nonparametric kernel-based model specification test that can be used when the regression model contains both discrete and continuous regressors. We employ discrete variable kernel functions and we smooth both the discrete and continuous regressors using least squares cross-validation (CV) methods. The test statistic is shown to have an asymptotic normal null distribution. We also prove the validity of using the wild bootstrap method to approximate the null distribution of the test statistic, the bootstrap being our preferred method for obtaining the null distribution in practice. Simulations show that the proposed test has significant power advantages over conventional kernel tests which rely upon frequency-based nonparametric estimators that require sample splitting to handle the presence of discrete regressors.

### MSC:

 62G10 Nonparametric hypothesis testing 62G08 Nonparametric regression and quantile regression 62E20 Asymptotic distribution theory in statistics 62G09 Nonparametric statistical resampling methods 65C60 Computational problems in statistics (MSC2010)
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### References:

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