THE THEIL-SEN ESTIMATOR WITH DOUBLY CENSORED-DATA AND APPLICATIONS TOASTRONOMY

The Theil-Sen estimator of the slope parameter in simple linear regres sion is extended to data with both the response and the covariate subj ect to censoring. Based on inverting a suitable version of Kendall's t au statistic, this estimator requires weak assumptions and is simple t o compute, and a simple estimate of its asymptotic variance is obtaine d. A second extension of the Theil-Sen estimator, based on a direct es timation of the median of pairwise slopes, is given. These estimators are compared numerically with versions of Schmitt's estimator and appl ied to two data sets from the recent astronomical literature.