Confidence Intervals based on Rank Statistics in Linear Models

Consider the linear models of which the distributions of the errors are non-normal. We propose a method based on rank statistics for constructing confidence intervals for the parameters in the linear models. It is found that the proposed confidence intervals have coverage probabilities which are fairly close to the target value. Furthermore when the skewness of the distributions is large, the expected lengths of the proposed confidence intervals are found to be much shorter than those of the percentile bootstrap confidence intervals, and the classical confidence intervals which are derived by assuming that the errors are normally distributed