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

The simple linear model $$Y_i = \alpha + \beta \, x_i + \epsilon _i$$ Y i = α + β x i + ϵ i $$(i=1,2, \ldots ,N \ge 2)$$ ( i = 1 , 2 , … , N ≥ 2 ) is considered, where the $$x_i$$ x i ’s are given constants and $$\epsilon _1, \epsilon _2 , \ldots , \epsilon _N$$ ϵ 1 , ϵ 2 , … , ϵ N are independent identically distributed (iid) with continuous distribution function F. An estimator $$\tilde{\beta }$$ β ~ of the slope parameter is proposed, based on a stochastic process which makes use of Gini’s cograduation index. The properties of $$\tilde{\beta }$$ β ~ and of the related confidence interval are studied. Some comparisons are given, in terms of asymptotic relative efficiency, with other estimators of $$\beta $$ β including that obtained with the method of least squares.