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: R.G. Vugrinovich
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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.
Suggested Citation
Vugrinovich, R., 1981, A distribution-free alternative to least-squares regression and its application to Rb/Sr isochron calculations: Journal of the International Association for Mathematical Geology, v. 13, no. 5, p. 443-454, https://doi.org/10.1007/BF01079647.
| 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 |