Abstract
In this study, we propose nonparametric testing for heteroscedasticity in nonlinear regression models based on pairwise distances between points in a sample. The test statistic can beformulated such that U-statistic theory can be applied to it. Although the limiting null distribution of the statistic iscomplicated, we can derive a computationally feasible bootstrap approximation forsuch a distribution; the validity of the introduced bootstrap algorithm is proven.The test can detect any local alternatives that are different fromthe null at a nearly optimal rate in hypothesis testing. Theconvergence rate of this test statistic does not depend on thedimension of the covariates, which significantly alleviates the impact ofdimensionality. We provide three simulation studies anda real-data example to evaluate the performance of the test anddemonstrate its applications.
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