A model specification test for the variance function in nonparametric regression. (English) Zbl 1427.62031
Summary: The problem of testing for the parametric form of the conditional variance is considered in a fully nonparametric regression model. A test statistic based on a weighted \(L_2\)-distance between the empirical characteristic functions of residuals constructed under the null hypothesis and under the alternative is proposed and studied theoretically. The null asymptotic distribution of the test statistic is obtained and employed to approximate the critical values. Finite sample properties of the proposed test are numerically investigated in several Monte Carlo experiments. The developed results assume independent data. Their extension to dependent observations is also discussed.
MSC:
| 62G08 | Nonparametric regression and quantile regression |
| 62G10 | Nonparametric hypothesis testing |
| 62E20 | Asymptotic distribution theory in statistics |
Keywords:
characteristic function; conditional variance models; nonparametric regression; regression residualsReferences:
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