Robustness assessment of pretest and shrinkage estimators in censored semiparametric linear models

{Asymptotic theory, influence diagnostics and Monte Carlo simulations are used to demonstrate the robustness and efficiency of pretest and shrinkage estimators in semiparametric censored regression models.} This paper introduces shrinkage estimators namely, the preliminary test estimator, Stein-type estimator, and positive-part Stein estimator for semiparametric censored regression models. We derive the asymptotic distributions of the estimators and the nonparametric component, along with their asymptotic mean square error (AMSE) matrices. A novel contribution is the extension of Cook's distance as an influence diagnostic tool for these estimators, using a case-deletion approach and weighting by the respective AMSE matrices. Simulation studies assess estimator risk across different censoring levels and evaluate the proposed diagnostics. The methodology is applied to lung cancer data to demonstrate its practical utility.