Finite-sample bias of Nelson–Aalen estimation
= Finite-sample bias of Nelson–Aalen estimation
Even with a common event hazard, the exact <expectation> of the <Nelson–Aalen estimator> is $\int_0^t\mathbb P(Y(u)>0)h(u)\,du$, because no increments can be observed after the <risk set> is empty. Replacing ratios by ratios of expectations gives an approximate target and does not prove finite-sample unbiasedness. For one uncensored exponential event time, the estimator has mean $1-e^{-\lambda t}$ rather than $\lambda t$.