  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.
