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  • Book
  • © 2013

L1-Norm and L∞-Norm Estimation

An Introduction to the Least Absolute Residuals, the Minimax Absolute Residual and Related Fitting Procedures

  • 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

Part of the book series: SpringerBriefs in Statistics (BRIEFSSTATIST)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-vi
  2. Introduction

    • Richard William Farebrother
    Pages 1-3
  3. Point Fitting Problems in One and Two Dimensions

    • Richard William Farebrother
    Pages 5-9
  4. The Hyperplane Fitting Problem in Two or More Dimensions

    • Richard William Farebrother
    Pages 11-19
  5. Linear Programming Computations

    • Richard William Farebrother
    Pages 21-29
  6. Statistical Theory

    • Richard William Farebrother
    Pages 31-36
  7. The Least Median of Squared Residuals Procedure

    • Richard William Farebrother
    Pages 37-41
  8. Mechanical Representations

    • Richard William Farebrother
    Pages 43-56
  9. Back Matter

    Pages 57-58

About this book

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.​

Authors and Affiliations

  • The University of Manchester, Manchester, United Kingdom

    Richard William Farebrother

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.

Bibliographic Information

Buy it now

Buying options

eBook USD 29.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 39.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access