Assessing the adequacy of variance function in heteroscedastic regression models

Heteroscedastic data arise in many applications. In heteroscedastic regression analysis, the variance is often modeled as a parametric function of the covariates or the regression mean. We propose a kernel-smoothing type nonparametric test for checking the adequacy of a given parametric variance structure. The test does not need to specify a parametric distribution for the random errors. It is shown that the test statistic has an asymptotical normal distribution under the null hypothesis and is powerful against a large class of alternatives. We suggest a simple bootstrap algorithm to approximate the distribution of the test statistic in finite sample size. Numerical simulations demonstrate the satisfactory performance of the proposed test. We also illustrate the application by the analysis of a radioimmunoassay data set.