Least Median of Squares Solution of Multiple Linear Regression Models Through the Origin

Atilgan Y., Gunay S.

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, vol.40, no.22, pp.4125-4137, 2011 (SCI-Expanded) identifier identifier


Barreto and Maharry (2006) showed that PROGRESS algorithm fails to find a correct minimum "Least Median of Squares/LMS" estimate for bivariate regression models which have no intercept. Kayhan and Gunay (2008) presented a different approach for the regression models through the origin which includes at most two unknown parameters. However, LMS estimate for multiple linear regression models still remains an open issue. The aim of this study is to show that finding true LMS estimate for zero intercept multiple linear regression models can be treated as a convex optimization problem and to provide a more general algorithm for any dimensional linear regression models.