Statistical inference on heteroscedastic models based on regression quantiles

For a class of heteroscedastic linear models in which the standard errors of response variables are linear in regressors, we construct confidence intervals and prediction intervals by the direct method and the studentization method, extending the results in Zhou and Portnoy (1994). Estimation of weights and a test of heteroscedasticity are based on LAD residuals. In the presence of replicated observations of response variables, we propose to estimate weights by regressing the local estimates of standard errors on regressors. Simulation results show that the direct method is robust against departures from assumptions on the error distribution. Estimation of weights based on replicated observations appear to be no better than those based on the LAD residuals.