 Likelihood support reduction under censoring

Partition the time axis into cells on which membership in each observed exact-event or censoring set is constant. Let $w_j$ be a cell's probability mass and $A_{ij}$ indicate whether cell $j$ is permitted by observation $i$. The empirical likelihood has the displayed form, with nonnegative masses summing to one. Columns of $A$ that agree can be combined. If column $j$ is componentwise dominated by another column $k$, moving all mass from $j$ to $k$ cannot reduce any factor, so an unconstrained nonparametric maximum-likelihood estimator can omit column $j$. The remaining log-likelihood is a concave function of the masses. Extra constraints can prevent a domination move; for a fixed survivor function value, split cells at the constrained time and retain the associated linear mass constraint.