Journal of Applied Mathematics and Decision Sciences 
Volume 2007 (2007), Article ID 37475, 15 pages
doi:10.1155/2007/37475
Research Article

An M-Estimation-Based Procedure for Determining the Number of Regression Models in Regression Clustering

C. R. Rao,1 Y. Wu,2 and Q. Shao3

 1Department of Statistics, Penn State University, University Park 16802, PA, USA
2Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto M3J 1P3, Ontario, Canada
3Novartis Pharmaceuticals Corporation, East Hanover 07936, NJ, USA
Received 16 June 2007; Accepted 16 July 2007

Recommended by Paul Cowpertwait

Abstract

In this paper, a procedure based on M-estimation to determine the number of regression models for the problem of regression clustering is proposed. We have shown that the true classification is attained when n increases to infinity under certain mild conditions, for instance, without assuming normality of the distribution of the random errors in each regression model.