Estimating Regression Coefficients by Minimizing the Dispersion of the Residuals
TLDR
In this article, the authors give some measures of the dispersion of a set of numbers, and define their estimates as those values of the parameters that minimize the residual dispersion, which is asymptotically equivalent to estimates recently proposed by Jureckova.Abstract:
An appealing approach to the problem of estimating the regression coefficients in a linear model is to find those values of the coefficients which make the residuals as small as possible. We give some measures of the dispersion of a set of numbers, and define our estimates as those values of the parameters which minimize the dispersion of the residuals. We consider dispersion measures which are certain linear combinations of the ordered residuals. We show that the estimates derived from them are asymptotically equivalent to estimates recently proposed by Jureckova. In the case of a single parameter, we show that our estimate is a "weighted median" of the pairwise slopes $(Y_j - Y_i)/(c^j - c^i)$.read more
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