Constraint-Adjusted Nonparametric Inference for Residual-Life Functionals Under Stochastic Precedence

Nonparametric inference for residual-life functionals is a fundamental problem in mathematical statistics, reliability theory, and survival analysis, particularly in studies with limited sample sizes where empirical plug-in estimators may exhibit substantial sampling variability. In comparative lifetime analysis, additional qualitative information is often available regarding the relative behavior of two populations; however, such information is frequently too weak to justify classical stochastic dominance assumptions. Stochastic precedence provides a natural and interpretable framework for representing this partial ordering through a pairwise probabilistic constraint. This paper develops a constraint-adjusted nonparametric inference framework for estimating the mean residual life (MRL) and quantile residual life (QRL) functions under stochastic precedence information. The proposed approach replaces the ordinary empirical distribution function in standard residual-life plug-in estimators with a constraint-adjusted empirical distribution function that enforces the stochastic precedence relation at the sample level. The adjustment is governed by a data-driven scaling factor and is asymptotically negligible, thereby preserving the large-sample behavior of the ordinary empirical estimators while incorporating meaningful structural information in finite samples. Strong consistency of the proposed MRL and QRL estimators was established under mild regularity conditions. A Monte Carlo study based on Weibull and gamma lifetime models demonstrates that in the simulation settings considered, the proposed estimators provide improved finite-sample stability and generally achieve smaller mean squared errors than their ordinary empirical counterparts, especially for small and moderate sample sizes. The methodology is further illustrated using survival data from patients with squamous cell carcinoma of the oropharynx, highlighting its practical relevance in biomedical survival analysis. The proposed method offers a flexible, interpretable, and computationally simple framework for nonparametric inference with structured lifetime data under weak stochastic ordering information.