Generalized Least-Powers Regressions I: Bivariate Regressions

Authors

Nataniel Greene, CUNY Kingsborough Community CollegeFollow

Document Type

Article

Publication Date

11-5-2016

Abstract

The bivariate theory of generalized least-squares is extended here to least-powers. The bivariate generalized least-powers problem of order p seeks a line which minimizes the average generalized mean of the absolute pth power deviations between the data and the line. Least-squares regressions utilize second order moments of the data to construct the regression line whereas least-powers regressions use moments of order p to construct the line. The focus is on even values of p, since this case admits analytic solution methods for the regression coefficients. A numerical example shows generalized least-powers methods performing comparably to generalized least-squares methods, but with a wider range of slope values.

Comments

This work was originally published in International Journal of Mathematical Models and Methods in Applied Sciences.