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

摘要

Let M(Y vertical bar X) = beta(0) + beta X-1 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 M(Y[X = X-i)(i = 1, ..., n) 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.