Evaluating the adequacy of variance function using pairwise distances

In this article, we develop a distance-based testing for assessing the adequacy of conditional variance function using pairwise distances. Under the null hypothesis, we state the limiting distribution of the proposed statistic, which is complicated. A resampling type statistic is proposed for approximating the null distribution, and we prove the validity of the resampling algorithm. The test could detect any local alternatives at a nearly optimal rate. Simulation studies are provided to examine the numerical performance of the proposed test, and a real data example is illustrated its application.