L1-Norm and L -Norm Estimation - An Introduction to the Least Absolute Residuals, the Minimax Absolute Residual and Related Fitting Procedures

This monograph is concerned with the fitting of linear relationships in the context of the linear statistical model. As alternatives to the familiar least squared residuals procedure, it investigates the relationships between the least absolute residuals, the minimax absolute residual and the least median of squared residuals procedures. It is intended for graduate students and research workers in statistics with some command of matrix analysis and linear programming techniques.

List of contents

Introduction.- Point Fitting Problems in One- and Two-dimensions.- The Hyperplane Fitting Problem in Two or More Dimensions.- Linear Programming Computations.- Statistical Theory.- The Least Median of Squared Residuals Procedure.- Mechanical Representations.- References.- Index of Names.

About the author

Dr. Richard William Farebrother was a member of the teaching staff of the Victoria University of Manchester 1970-1993 and an Honorary Reader in Econometrics 1993-2001. He has published three books: Linear Least Squares Computations (1988), Fitting Linear Relationships (1999), and Visualizing Statistical Models and Concepts (2002). He has also published more than 150 research papers.

Summary

This monograph is concerned with the fitting of linear relationships in the context of the linear statistical model. As alternatives to the familiar least squared residuals procedure, it investigates the relationships between the least absolute residuals, the minimax absolute residual and the least median of squared residuals procedures. It is intended for graduate students and research workers in statistics with some command of matrix analysis and linear programming techniques.

Product details

• Authors: Richard Farebrother, Richard William Farebrother
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 30.01.2013
• EAN: 9783642362996
• ISBN: 978-3-642-36299-6
• No. of pages: 58
• Dimensions: 156 mm x 5 mm x 236 mm
• Weight: 122 g
• Illustrations: VI, 58 p.
• Series: SpringerBriefs in Statistics; SpringerBriefs in Statistics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics; Algebra, C, History, Statistics, Mathematics, geometry, Mathematics and Statistics, Classical mechanics, Statistical Theory and Methods, Linear Algebra, Mechanics, History of mathematics, History of Mathematical Sciences, Matrix theory, Linear and Multilinear Algebras, Matrix Theory