## The Annals of Mathematical Statistics

### Estimating Regression Coefficients by Minimizing the Dispersion of the Residuals

Louis A. Jaeckel

#### 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 $(Y_j - Y_i)/(c^j - c^i)$.

#### Article information

Source
Ann. Math. Statist. Volume 43, Number 5 (1972), 1449-1458.

Dates
First available in Project Euclid: 27 April 2007

http://projecteuclid.org/euclid.aoms/1177692377

Digital Object Identifier
doi:10.1214/aoms/1177692377

Mathematical Reviews number (MathSciNet)
MR348930

Zentralblatt MATH identifier
0277.62049

JSTOR