Confidence intervals for two robust regression lines with a heteroscedastic error term

Recently, Wilcox (1994) suggested a method of computing a confidence interval for the slope of two robust regression methods. Results from Wu (1986) suggest that Wilcox's method will fail when the error term has non-constant variance and simulations reported here confirm this. This paper describes a more satisfactory method for handling non-constant variance when working with the biweight midregression line considered by Wilcox, with little or no loss in accuracy when the error term has constant variance. Moreover, this paper illustrates that the biweight midregression method, in its present form, can yield an unsatisfactory estimate of the slope when there is a heteroscedastic error term, even with a very large sample size. A Simple method of correcting this problem is described which also eliminates the need for the bias correction term used by Wilcox. This paper also considers the problem of computing confidence intervals for the slope of the robust regression method derived by De Jongh, De Wet and Welsh (1988), and a fairly accurate method is found even when the error term has non-constant variance.