Heteroscedasticity testing for regression models: A dimension reduction-based model adaptive approach

Heteroscedasticity testing is of importance in regression analysis. Existing local smoothing tests suffer severely from curse of dimensionality even when the number of covariates is moderate because of use of nonparametric estimation. A dimension reduction-based model adaptive test is proposed which behaves like a local smoothing test as if the number of covariates was equal to the number of their linear combinations in the mean regression function, in particular, equal to 1 when the mean function contains a single index. The test statistic is asymptotically normal under the null hypothesis such that critical values are easily determined. The finite sample performances of the test are examined by simulations and a real data analysis.