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Birkhäuser

Least Absolute Deviations

Theory, Applications and Algorithms

  • Book
  • © 1983

Overview

Authors:
  1. Peter Bloomfield

    1. Department of Statistics, North Carolina State Unversity, Raleigh, USA

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    You can also search for this author in PubMed   Google Scholar

  2. William L. Steiger

    1. Department of Computer Science, Rutgers University, New Brunswick, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Progress in Probability (PRPR, volume 6)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xiv
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  2. Generalities

    • Peter Bloomfield, William L. Steiger
    Pages 1-36

  3. LAD in Linear Regression

    • Peter Bloomfield, William L. Steiger
    Pages 37-76

  4. LAD in Autoregression

    • Peter Bloomfield, William L. Steiger
    Pages 77-108

  5. LAD in Multi-Way Tables

    • Peter Bloomfield, William L. Steiger
    Pages 109-130

  6. LAD Spline Fitting

    • Peter Bloomfield, William L. Steiger
    Pages 131-151

  7. LAD and Linear Programming

    • Peter Bloomfield, William L. Steiger
    Pages 152-180

  8. Algorithms for LAD

    • Peter Bloomfield, William L. Steiger
    Pages 181-274

  9. Appendix

    • Peter Bloomfield, William L. Steiger
    Pages 276-325

  10. Back Matter

    Pages 326-351
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Keywords

About this book

Least squares is probably the best known method for fitting linear models and by far the most widely used. Surprisingly, the discrete L 1 analogue, least absolute deviations (LAD) seems to have been considered first. Possibly the LAD criterion was forced into the background because of the com­ putational difficulties associated with it. Recently there has been a resurgence of interest in LAD. It was spurred on by work that has resulted in efficient al­ gorithms for obtaining LAD fits. Another stimulus came from robust statistics. LAD estimates resist undue effects from a feyv, large errors. Therefore. in addition to being robust, they also make good starting points for other iterative, robust procedures. The LAD criterion has great utility. LAD fits are optimal for linear regressions where the errors are double exponential. However they also have excellent properties well outside this narrow context. In addition they are useful in other linear situations such as time series and multivariate data analysis. Finally, LAD fitting embodies a set of ideas that is important in linear optimization theory and numerical analysis. viii PREFACE In this monograph we will present a unified treatment of the role of LAD techniques in several domains. Some of the material has appeared in recent journal papers and some of it is new. This presentation is organized in the following way. There are three parts, one for Theory, one for Applicatior.s and one for Algorithms.

Authors and Affiliations

  • Department of Statistics, North Carolina State Unversity, Raleigh, USA

    Peter Bloomfield

  • Department of Computer Science, Rutgers University, New Brunswick, USA

    William L. Steiger

Bibliographic Information

  • Book Title: Least Absolute Deviations

  • Book Subtitle: Theory, Applications and Algorithms

  • Authors: Peter Bloomfield, William L. Steiger

  • Series Title: Progress in Probability

  • DOI: https://doi.org/10.1007/978-1-4684-8574-5

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1983

  • Softcover ISBN: 978-1-4684-8576-9Published: 12 December 2012

  • eBook ISBN: 978-1-4684-8574-5Published: 06 December 2012

  • Series ISSN: 1050-6977

  • Series E-ISSN: 2297-0428

  • Edition Number: 1

  • Number of Pages: XIV, 351

  • Topics: Probability Theory and Stochastic Processes, Algorithms, Applications of Mathematics

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