Confidence intervals based on robust regression

In this paper, we consider constructing reliable confidence intervals for regression parameters using robust M-estimation allowing for the possibility of time series correlation among the errors. The change of variance function is used to approximate the theoretical coverage for confidence intervals based on uncorrelated errors. Bootstrap techniques for dependent data and weighted empirical adaptive variance estimators are used to construct three variance estimates. A simulation study is conducted to investigate the performance of those variance estimates for small and large sample sizes. In particular, the simulated empirical coverages are examined for various models of correlated errors. Our procedures show improvement over intervals based on independence but do illustrate the need for caution in carrying out inference in linear models for moderate sample sizes if correlation among the errors is suspected. (C) 2002 Elsevier Science B.V. All rights reserved.