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.

翻译：在本文中,我们提出了基于非线性和非线性和非线性回归模型中的距离共变值来检查有条件差异的参数形式的新测试。 从远距离共变的好特性中继承我们的测试在实际中非常容易实施,但因共变的维度影响较小。根据无效假设和替代假设来调查试验统计的无症状特性。我们表明,拟议的测试与任何替代假设都是一致的,并能够发现与非线性和非线性性性性环境的1/root(n)参数率/root(n)的无效假设相融合的地方替代物。由于限制试验统计的无效分布是难以解决的,我们建议用一个残留的靴子来大致限制无线分布。我们提出了模拟研究,以评估拟议测试的有限样本性能。我们还将拟议的测试应用于一个真实的数据集,用于说明。