thumbnail

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

Journal of the International Association for Mathematical Geology

By:
DOI: 10.1007/BF01079647

Links

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
First page:
443
Last page:
454
Number of Pages:
12