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

### Abstract

The simple linear model $$Y_i = \alpha + \beta \, x_i + \epsilon_i \qquad i=1,2, \ldots,N \geq 2$$ is considered, where the $x_i$'s are given constants and $\epsilon_1, \epsilon_2 , \ldots, \epsilon_N$ 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 $\tilde{\beta} = \frac 12 \, \left\{ \sup (b: G(\underline y;b) >0) + \right.$ $\left. \inf (b: G(\underline y;b) <0) \right\}.$ 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.Comment: Translation from Italian of the paper: Cifarelli, D.M. (1978). "La stima del coefficiente di regressione mediante l'indice di cograduazione di Gini

Topics: Statistics - Methodology
Year: 2014
OAI identifier: oai:arXiv.org:1411.4809

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