Distribution-free interval estimation techniques for slope in simple linear regression



Journal Title

Journal ISSN

Volume Title


Texas Tech University


This work is concerned with estimating the slope parameter, B, in the simple linear regression model. Many of the rank procedures used to find confidence intervals for fl are free of distributional assumptions on the dependent variable. Rank procedures often generate smaller intervals than those given by the classical procedures when the residual distribution is skewed or heavy-tailed. Many of these procedures, such as those discussed by Theil, Sen, and Sievers, are computationally infeasible, even for a computer, when used with samples much larger than 100. This dissertation develops distribution-free procedures which substantially reduce these calculations. The rank-based procedures of Theil, Sen, and Sievers require n(n-1)/2 pairwise slopes to be computed. The new procedures require only n such pairwise slopes to be computed, a comparatively negligible amount of computation. Measures of asymptotic relative efficiency (ARE) and finite sample efficiency are derived and used to evaluate these "reduced" procedures. In many cases, the reduced procedures have efficiencies of .8 when compared to the procedures described by Theil, Sen, and Sievers. This is a small loss considering the computational gains from using the reduced procedures developed in this dissertation.



Nonparametric statistics, Regression analysis, Estimation theory, Distribution free methods (Mathematical statistics