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

Abstract

The simple linear model $$Y_i=\alpha +\beta x_i+{\epsilon }_{i}i=1,2,\dots ,N\ge 2$$ is considered, where the $x_i$'s are given constants and ${\epsilon }_1,{\epsilon }_2,\dots ,{\epsilon }_N$ are iid with continuous distribution function $F$. An estimator of $\beta$ is proposed, based on Gini's rank association coefficient $G(\underline{y};b)$ and defined as $\tilde{\beta }=\frac{1}{2}\{\sup (b:G(\underline{y};b)>0)+$ $\inf (b:G(\underline{y};b)<0)\}.$ The properties of $\tilde{\beta }$ 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.

arXiv commentTranslation from Italian of the paper: Cifarelli, D.M. (1978). "La stima del coefficiente di regressione mediante l'indice di cograduazione di Gini"