On Edgeworth´s method for minimum absolute error linear regression

Author

Hawley, Robert W. ; Gallagher, Neal C., Jr.

Author_Institution

Sandia Nat. Labs., Albuquerque, NM, USA

Volume

42

Issue

8

fYear

1994

fDate

8/1/1994 12:00:00 AM

Firstpage

2045

Lastpage

2054

Abstract

The Edgeworth (1887) algorithm for minimizing absolute error is known to suffer from convergence problems when the data contains degeneracies. In this paper, it is shown that for the particular problem of fitting a line to a set of uniformly sampled data, the problem of degeneracy may be easily avoided by utilizing a stable sorter for the weighted median operation needed in Edgeworth´s method. Proof of convergence is based on establishing an equivalence between the use of a stable sorting routine and perturbing the original data in such a way that no degeneracies exist. In addition, it will be shown that the data set size may be selected so that the minimum error fit is unique

Keywords

convergence of numerical methods; error analysis; linear algebra; sorting; statistical analysis; Edgeworth algorithm; Edgeworth´s method; convergence; minimum absolute error linear regression; minimum error fit; stable sorter; stable sorting routine; uniformly sampled data; weighted median operation; Chaotic communication; Convergence; Fading; Frequency estimation; Linear regression; Noise robustness; Phase estimation; Phase locked loops; Signal processing algorithms; Sorting;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.301827

Filename

301827