R-Estimation with Right-Censored Data

2026-01-10

AI Summary

This study addresses robust estimation in linear models with right-censored data by rigorously extending R-estimators to this setting for the first time. By constructing rank-based estimating equations tailored to censored outcomes, the framework naturally incorporates both linear (e.g., Wilcoxon) and bounded nonlinear rank score functions, and establishes their equivalence to the Ritov–Tsiatis class of estimating equations. A key innovation lies in the introduction of self-consistent residual distributions and midpoint cumulative distribution functions—along with their generalizations—combined with a self-consistency algorithm to implement the estimator. Theoretical analysis establishes the asymptotic properties of the proposed estimator and provides a feasible variance estimation method, thereby laying a rigorous foundation for robust inference and delivering a practical tool for analyzing right-censored data.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Measurement, analysis, and circumvention of Web censorship

Abstract

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.

Problem

• R-estimation
• right-censored data
• linear model
• rank-based estimation
• survival analysis

Innovation

• R-estimation
• right-censored data
• rank-based inference
• estimating equations
• nonlinear-in-ranks scores