A study of several new and existing tests for heteroscedasticity in the general linear model1

Several optimum non-parametric tests for heteroscedasticity are proposed and studied along with the tests introduced in the literature in terms of power and robustness properties. It is found that all tests are reasonably robust to the Ordinary Least Squares (OLS) residual estimates, number and character of the regressors. Only a few are robust to both the distributional and independence assumptions about the errors. The power of tests can be improved with the OLS residual estimates, the increased sample size and the variability of the regressors. It can be substantially reduced if the observations are not normally distributed, and may increase or decrease if the errors are dependent. Each test is optimum to detect a specific form of heteroscedasticity and a serious power loss may occur if the underlying heteroscedasticity assumption in the data generation deviates from it.