Linear regression: robust heteroscedastic confidence bands that have some specified simultaneous probability coverage

Abstract

ABSTRACTLet be some conditional measure of location associated with the random variable Y, given X, where the unknown parameters and are estimated based on the random sample . When using the ordinary least squares (OLS) estimator and , several methods for computing a confidence band have been derived that are aimed at achieving some specified simultaneous probability coverage assuming a homoscedastic error term and normality. There is an extant technique that allows heteroscedasticity, but a remaining concern is that the OLS estimator is not robust. Extant results indicate how a confidence interval can be computed via a robust regression estimator when there is heteroscedasticity and attention is focused on a single value of X. The paper extends this method by describing a heteroscedastic technique for computing a confidence interval for each () such that the simultaneous probability coverage has some specified value. The small-sample properties of the method are studied when using the OLS estimators as well as three robust regression estimators.