L1-Norm and L∞-Norm Estimation, 2013
An Introduction to the Least Absolute Residuals, the Minimax Absolute Residual and Related Fitting Procedures
SpringerBriefs in Statistics Series

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Language: English

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58 p. · 15.5x23.5 cm · Paperback

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.?

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. ​  
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.
Single source of information about this important area of research Wide-ranging discussion of least absolute residuals, minimax residual and least median of squared residuals fitting procedures Several new results not previously published in book form Includes supplementary material: sn.pub/extras