Confidence intervals for the slope of a regression line when the error term has nonconstant variance

摘要

Nanayakkara and Cressie (1991) suggest a general approach to computing a confidence interval for the slope in the usual regression model when the error term has nonconstant variance. Their simulations for the case of a single predictor indicate that when the predictor has fixed values that are equally spaced, and the error term is normal with variance a function of the predictor variable, their method provides fairly accurate probability coverage. This paper extends their results by considering the case where the predictor is a random variable, and where both the predictor and error term have nonnormal distributions. Four bootstrap methods are also considered. Only one of the methods considered in this paper gives reasonably accurate probability coverage for all the situations considered in the simulations. It is based on a modified percentile-bootstrap technique.