There exist many investigations on curve estimation in right-censored and complete data under shape constraints. In contrast, researchers rarely have paid attention to such estimations under the random left truncation model. To the best of our knowledge, the previous researches contain no result on the non-parametric estimation of a hazard function from this model under monotone constraint using unconditional likelihood. Here, we derive an estimator that maximizes the likelihood function over the set of all non-increasing right-continuous step-wise hazard functions for estimating increasing hazard function. Additionally, we studied large sample properties of our proposed estimator and the small sample behavior of it using simulated data.

Keywords