TY - JOUR
T1 - The Theil-Sen estimator with doubly censored data and applications to astronomy
AU - Akritas, Michael G.
AU - Murphy, Susan A.
AU - LaValley, Michael P.
N1 - Funding Information:
* Michael G. Akritas is Professor and Susan A. Murphy is Assistant Professor, Department of Statistics, Pennsylvania State University, University Park, PA 16802. Michael P. LaValley is Postdoctoral Research Fellow, Department of Biostatistics, Harvard School of Public Health, Boston, MA 02 1 15. This research was supported in part by Grants DMS-90077 I7 and DMS-9208066 from the National Science Foundation. The authors are grateful to Eric D. Feigelson for providing the astronomical data sets and to the associate editor and the referees for helpful comments.
PY - 1995/3
Y1 - 1995/3
N2 - 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.
AB - 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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U2 - 10.1080/01621459.1995.10476499
DO - 10.1080/01621459.1995.10476499
M3 - Article
AN - SCOPUS:21844506903
SN - 0162-1459
VL - 90
SP - 170
EP - 177
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
IS - 429
ER -