On the behavior of the Lynden-Bell estimator in widely orthant-dependent model

This article is devoted to investigating some asymptotic properties of the Lynden-Bell and the cumulative risk function estimators when the survival and the truncated times form widely orthant-dependent sequences. As main results, we establish strong uniform consistency rates for the proposed estimators. Then, as an application, we derive a strong uniform consistency rate for the hazard rate function estimator. The performances of the proposed estimators are illustrated via some simulations.