A test for the parametric form of the variance function in a partial linear regression model. (English) Zbl 1140.62029
Summary: We consider the problem of testing for a parametric form of the variance function in a partial linear regression model. A new test is derived, which can detect local alternatives converging to the null hypothesis at a rate \(n^{-1/2}\) and is based on a stochastic process of the integrated variance function. We establish weak convergence to a Gaussian process under the null hypothesis, fixed and local alternatives. In the special case of testing for homoscedasticity the limiting process is a scaled Brownian bridge. We also compare the finite sample properties with a test based on an \(L^{2}\)-distance, which was recently proposed by J. You and G. Chen [Testing heteroscedasticity in partially linear regression models. Stat. Probab. Lett. 73, No. 1, 61–70 (2005; Zbl 1101.62033)].
MSC:
| 62G08 | Nonparametric regression and quantile regression |
| 62J05 | Linear regression; mixed models |
| 60F05 | Central limit and other weak theorems |
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 62G10 | Nonparametric hypothesis testing |
Citations:
Zbl 1101.62033References:
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