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The Theil-Sen Estimator With Doubly Censored Data and Applications to Astronomy

Michael G. Akritas, Susan A. Murphy and Michael P. LaValley
Journal of the American Statistical Association
Vol. 90, No. 429 (Mar., 1995), pp. 170-177
DOI: 10.2307/2291140
Stable URL: http://www.jstor.org/stable/2291140
Page Count: 8
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The Theil-Sen Estimator With Doubly Censored Data and Applications to Astronomy
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Abstract

The Theil-Sen estimator of the slope parameter in simple linear regression is extended to data with both the response and the covariate subject to censoring. Based on inverting a suitable version of Kendall's τ statistic, this estimator requires weak assumptions and is simple to compute, and a simple estimate of its asymptotic variance is obtained. A second extension of the Theil-Sen estimator, based on a direct estimation of the median of pairwise slopes, is given. These estimators are compared numerically with versions of Schmitt's estimator and applied to two data sets from the recent astronomical literature.

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