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arXiv · 1411.4809

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

D. M. Cifarelli
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Abstract

The simple linear model $$Y_i = α+ β\, x_i + ε_i \qquad i=1,2, \ldots,N \geq 2$$ is considered, where the $x_i$'s are given constants and $ε_1, ε_2 , \ldots, ε_N$ are iid with continuous distribution function $F$. An estimator of $β$ is proposed, based on Gini's rank association coefficient $G(\underline y;b)$ and defined as $\tildeβ = \frac 12 \, \left\{ \sup (b: G(\underline y;b) >0) + \right. $ $ \left. \inf (b: G(\underline y;b) <0) \right\}.$ The properties of $\tildeβ$ and of the related confidence interval are studied. Some comparisons are given, in terms of asymptotic relative efficiency, with other estimators of $β$ including that obtained with the method of least squares.

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D. M. Cifarelli. 2014-11-18. Estimation of the regression slope by means of Gini's cograduation index. https://arxiv.org/abs/1411.4809

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