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      On a non-parametric confidence interval for the regression slope

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          Abstract

          We investigate an application of the Tukey's methodology in Theil's regression to obtain a confidence interval for the true slope in the straight line regression model. This specific approach 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's tau, seriously deflates the true confidence level of the resulting interval. We provide also rigorous proofs in case of four data points (in general) and in case of five data points (under uniform distribution of errors). Summing up, we demonstrate that one should never combine statistical methods without checking the assumptions of their usage and we also give a warning to the already wide community of R users of Theil's regression from various fields of science.

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          Author and article information

          Journal
          2015-02-23
          2016-01-15
          1502.06412

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

          Custom metadata
          62G08, 62G15, 62G30
          Changes in Version 2 (results unchanged): (1) added references to the usage of the R package "mblm" in other sciences; (2) expanded Abstract and Introduction; (3) updated affiliation of the first author. Changes in Version 3 (results unchanged): (1) Section 6 slightly reorganized, since Condition 2 is now itroduced at a later stage; (2) true confidence levels of the Theil's CI added to Table 1
          stat.ME

          Methodology

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