On the solution of the errors in variables problem using the l1 norm

G. A. Watson, Ka Fai Cedric Yiu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

10 Citations (Scopus)

Abstract

A fundamental problem in data analysis is that of fitting a given model to observed data. It is commonly assumed that only the dependent variable values are in error, and the least squares criterion is often used to fit the model. When significant errors occur in all the variables, then an alternative approach which is frequently suggested for this errors in variables problem is to minimize the sum of squared orthogonal distances between each data point and the curve described by the model equation. It has long been recognized that the use of least squares is not always satisfactory, and the l1 criterion is often superior when estimating the true form of data which contain some very inaccurate observations. In this paper the measure of goodness of fit is taken to be the l1 norm of the errors. A Levenberg-Marquardt method is proposed, and the main objective is to take full advantage of the structure of the subproblems so that they can be solved efficiently.
Original languageEnglish
Pages (from-to)697-710
Number of pages14
JournalBIT
Volume31
Issue number4
DOIs
Publication statusPublished - 1 Dec 1991
Externally publishedYes

Keywords

  • AMS subject classification: 65D10, 65K05

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics
  • Software
  • Computer Graphics and Computer-Aided Design

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