论文标题
基于距离协方差测试回归中条件差异的参数形式
Testing the parametric form of the conditional variance in regressions based on distance covariance
论文作者
论文摘要
在本文中，我们提出了一项新的测试，以根据非线性和非参数回归模型中的距离协方差检查条件差异的参数形式。从距离协方差的良好属性继承，我们的测试在实践中很容易实现，并且对协变量的维度影响较小。测试统计数据的渐近特性在零和替代假设下进行了研究。我们表明，所提出的测试与任何替代方案都是一致的，并且可以在非线性和非参数设置中以参数速率1/root（n）收敛到零假设的局部替代方案。由于测试统计量的限制无效分布是棘手的，因此我们提出了一个残留的bootstrap，以近似限制零分布。提出了仿真研究，以评估拟议测试的有限样本性能。我们还将提出的测试应用于用于插图的真实数据集。
In this paper, we propose a new test for checking the parametric form of the conditional variance based on distance covariance in nonlinear and nonparametric regression models. Inherit from the nice properties of distance covariance, our test is very easy to implement in practice and less effected by the dimensionality of covariates. The asymptotic properties of the test statistic are investigated under the null and alternative hypotheses. We show that the proposed test is consistent against any alternative and can detect local alternatives converging to the null hypothesis at the parametric rate 1/root(n) in both the nonlinear and nonparametric settings. As the limiting null distribution of the test statistic is intractable, we propose a residual bootstrap to approximate the limiting null distribution. Simulation studies are presented to assess the finite sample performance of the proposed test. We also apply the proposed test to a real data set for illustration.
