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Estimates of the Regression Coefficient Based on Kendall's Tau

Pranab Kumar Sen
Journal of the American Statistical Association
Vol. 63, No. 324 (Dec., 1968), pp. 1379-1389
DOI: 10.2307/2285891
Stable URL: http://www.jstor.org/stable/2285891
Page Count: 11
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Estimates of the Regression Coefficient Based on Kendall's Tau
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Abstract

The least squares estimator of a regression coefficient β is vulnerable to gross errors and the associated confidence interval is, in addition, sensitive to non-normality of the parent distribution. In this paper, a simple and robust (point as well as interval) estimator of β based on Kendall's [6] rank correlation tau is studied. The point estimator is the median of the set of slopes (Yj - Yi)/(tj - ti) joining pairs of points with ti≠ tj, and is unbiased. The confidence interval is also determined by two order statistics of this set of slopes. Various properties of these estimators are studied and compared with those of the least squares and some other nonparametric estimators.

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