Method of averages as an alternative to \(L_ 1\)- and \(L_ 2\)-norm methods in special linear regression problems (Q1094796)

The very simple regression criterion of the method of averages requires that the sum of the first powers of the residuals be equal to zero in as many groups, as there are unknown parameters in the regression function. Since the residuals can be assigned to groups in several ways, this criterion is not unambiguous. This paper describes a rule for optimal grouping of residuals for a linear regression function of one independent variable. Briefly we mention relations which enable us to consider the main statistical properties of the method of averages. More favourable numerical features of the method of averages in comparison with both \(L_ 1\)- and \(L_ 2\)- norm methods are pointed out and some examples for linear regression functions are given.