The author considers a semiparametric linear regression model with right censored data where the error variables have an unknown density \(f_ 0\). The aim is to estimate the slope parameter \(\beta\). There are several approaches in the literature. The author suggests an estimator of Buckley-James type [J. Buckley and I. James, Biometrika 66, 429-436 (1979; Zbl 0425.62051)] which is a suitable modification of the M-estimate in regression. It is shown that this estimator is \(\sqrt{n}\)- consistent, asymptotically normal and that the estimator is asymptotically equivalent to an approach of A. A. Tsiatis [Ann. Stat. 18, No.1, 354-372 (1990; Zbl 0701.62051)].
The latter statement is based on an equivalence result between Doob-type martingales and counting process martingales by the author and J. A. Wellner [Statistical inference from stochastic processes, Proc. AMS-IMS- SIAM Jt. Summer Res. Conf., Ithaca/NY 1987, Contemp. Math. 80, 191-219 (1988; Zbl 0684.62072)].