Linear rank statistics in regression analysis with censored or truncated data (Q1190554)

The linear regression model \(y_ i = \beta^ Tx_ i + \varepsilon_ i\) \(i = 1,2, \dots\), is considered and estimation of \(\beta\) is studied for censored and truncated \(y_ i\)'s. According to the authors, ``Starting with the censored regression model we first review some recent work of \textit{A. A. Tsiatis} [Ann. Stat. 18, No. 1, 354-372 (1990; Zbl 0701.62051)] to construct and analyse rank estimators, in which the major difficulty lies in establishing the asymptotic linearity of the associated rank statistics. We then show that this difficulty can be handled more easily and in much greater generality by using a different approach, which we developed in J. Multivariate Anal. 27, No. 2, 334-358 (1988; Zbl 0684.62048), independently of Tsiatis' work, based on a tightness lemma for stochastic integrals of empirical-type processes ... Our approach can be easily extended to the truncated regression model ... and is also applicable to other kinds of nonparametric estimators''.