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R-Estimation with Right-Censored Data

This paper considers the problem of directly generalizing the R-estimator under a linear model formulation with right-censored outcomes. We propose a natural generalization of the rank and corresponding estimating equation for the R-estimator in the case of the Wilcoxon (i.e., linear-in-ranks) score function, and show how it can respectively be exactly represented as members of the classes of estimating equations proposed in Ritov (1990) and Tsiatis (1990). We then establish analogous results for a large class of bounded nonlinear-in-ranks score functions. Asymptotics and variance estimation are obtained as straightforward consequences of these representation results. The self-consistent estimator of the residual distribution function, and the mid-cumulative distribution function (and, where needed, a generalization of it), play critical roles in these developments.