A distribution-free alternative to least-squares regression and its application to Rb/Sr isochron calculations

Journal of the International Association for Mathematical Geology
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Abstract

A distribution-free estimator of the slope of a regression line is introduced. This estimator is designated Sm and is given by the median of the set of n(n - 1)/2 slope estimators, which may be calculated by inserting pairs of points (Xi, Yi)and (Xj, Yj)into the slope formula Si = (Yi - Yj)/(Xi - Xj), 1 ??? i < j ??? n Once Sm is determined, outliers may be detected by calculating the "residuals" given by Ri = Yi - SmXi where 1 ??? i ??? n, and chosing the median Rm. Outliers are defined as points for which |Ri - Rm| > k (median {|Ri - Rm|}). If no outliers are found, the Y-intercept is given by Rm. Confidence limits on Rm and Sm can be found from the sets of Ri and Si, respectively. The distribution-free estimators are compared with the least-squares estimators now in use by utilizing published data. Differences between the least-squares and distribution-free estimates are discussed, as are the drawbacks of the distribution-free techniques. ?? 1981 Plenum Publishing Corporation.

Additional publication details

Publication type Article
Publication Subtype Journal Article
Title A distribution-free alternative to least-squares regression and its application to Rb/Sr isochron calculations
Series title Journal of the International Association for Mathematical Geology
DOI 10.1007/BF01079647
Volume 13
Issue 5
Year Published 1981
Language English
Publisher location Kluwer Academic Publishers-Plenum Publishers
Larger Work Type Article
Larger Work Subtype Journal Article
Larger Work Title Journal of the International Association for Mathematical Geology
First page 443
Last page 454
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