Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 207 / 4 / c / Solution

Aggregate the individual increments. At an event time $x_i$, their conditional expectation is the numberat risk times $dH(x_i)$. Replacing expectation by the observed event increment gives $d\hat{H}(x_i)=v_i/r_i$. Thus the estimator is the Nelson–Aalen estimator