Coverage probabilities of confidence intervals for the slope parameter of linear regression model when the error term is not normally distributed

Abstract

Confidence interval for the slope parameter based on the t-statistic is not appropriate when the error term is not normally distributed. In this paper, we examine some existing methods for the interval estimation of the slope parameter and suggest new methods for giving better coverage accuracy. The following methods are considered: the standard t, the bootstrap-t, and three intervals based on the transformations of the t-statistic. The results for the Exponential and Weibull distributions and for the real data set are presented. The simulation study shows that these introduced intervals give better results than existing methods.