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 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 40 Issue: 22
  • Publication Date: 2011
  • Doi Number: 10.1080/03610926.2010.505691
  • Journal Name: COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.4125-4137

Abstract

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.