On a non-parametric confidence interval for the regression slope

摘要

We investigate an application of the Tukey's methodology in Theil'sregression to obtain a confidence interval for the true slope in the straightline regression model with not necessarily normal errors. This specificapproach is implemented since 2005 in a package of the software R; however,without any theoretical background. We illustrate by Monte Carlo simulations,that this methodology, unlike the classical Theil's approach based on Kendall'stau, seriously deflates the true confidence level of the resulting interval. Weprovide also rigorous proofs in case of four data points (in general) and incase of five data points (under some additional conditions); together with areal life methods usage example in the latter case. Summing up, we demonstratethat one should never combine statistical methods without checking theassumptions of their usage and we also give a warning to the already widecommunity of R users of Theil's regression from various fields of science.