Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: A Maximum Likelihood Approach to Least Absolute Deviation Regression | EURASIP Journal on Applied Signal Processing 2004 12 1762-1769 2004 Hindawi Publishing Corporation A Maximum Likelihood Approach to Least Absolute Deviation Regression Yinbo Li Department of Electrical and Computer Engineering University of Delaware Newark DE 19716 3130 USA Email yli@ Gonzalo R. Arce Department of Electrical and Computer Engineering University of Delaware Newark DE 19716 3130 USA Email arce@ Received 7 October 2003 Revised 22 December 2003 Least absolute deviation LAD regression is an important tool used in numerous applications throughout science and engineering mainly due to the intrinsic robust characteristics of LAD. In this paper we show that the optimization needed to solve the LAD regression problem can be viewed as a sequence of maximum likelihood estimates MLE of location. The derived algorithm reduces to an iterative procedure where a simple coordinate transformation is applied during each iteration to direct the optimization procedure along edge lines of the cost surface followed by an MLE of location which is executed by a weighted median operation. Requiring weighted medians only the new algorithm can be easily modularized for hardware implementation as opposed to most of the other existing LAD methods which require complicated operations such as matrix entry manipulations. One exception is Wesolowsky s direct descent algorithm which among the top algorithms is also based on weighted median operations. Simulation shows that the new algorithm is superior in speed to Wesolowsky s algorithm which is simple in structure as well. The new algorithm provides a better tradeoff solution between convergence speed and implementation complexity. Keywords and phrases least absolute deviation linear regression maximum likelihood estimation weighted median filters. 1. INTRODUCTION Linear regression has long been dominated by least squares LS techniques mostly due to their elegant theoretical foundation and ease of .
