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

Barreto and Maharry (2006 Barreto , H. , Maharry , D. ( 2006 ). Least median of squares and regression through the origin . Comput. Statist. Data Anal. 50 : 1391 – 1397 .[Crossref], [Web of Science ®] , [Google Scholar]) 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 Kayhan , Y. , Gunay , S. ( 2008 ). A new approach to least median of squares and regression through the origin . Commun. Statist. Theor. Meth. 37 ( 5 ): 773 – 781 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) 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.