Estimation of the regression slope by means of Gini's cograduation index

The simple linear model $$Y_i=\alpha +\beta x_i+{ϵ}_{i}i=1,2,\dots ,N\ge 2$$ is considered, where the $x_i$’s are given constants and ${ϵ}_1,{ϵ}_2,\dots ,{ϵ}_N$ are iid with continuous distribution function $F$. An estimator of $\beta$ is proposed, based on Gini’s rank association coefficient $G(\underset{‾}{y};b)$ and defined as $\tilde{\beta} = \frac 12 , \left{ \sup (b: G(\underline y;b) >0) + \right. $ $ \left. \inf (b: G(\underline y;b) <0) \right}.$Thepropertiesof$\tilde{\beta}$ and of the related confidence interval are studied. Some comparisons are given, in terms of asymptotic relative efficiency, with other estimators of $\beta$ including that obtained with the method of least squares.