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

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.​ Front Matter....Pages i-vi Introduction....Pages 1-3 Point Fitting Problems in One and Two Dimensions....Pages 5-9 The Hyperplane Fitting Problem in Two or More Dimensions....Pages 11-19 Linear Programming Computations....Pages 21-29 Statistical Theory....Pages 31-36 The Least Median of Squared Residuals Procedure....Pages 37-41 Mechanical Representations....Pages 43-56 Back Matter....Pages 57-58 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. ​ .