= Solution
Define the event <counting process> and <at-risk process> by
$$
N_i(u)=v_i\mathbf1\{x_i\leq u\},\qquad Y_i(u)=\mathbf1\{x_i\geq u\},\qquad
N(u)=\sum_iN_i(u),\quad Y(u)=\sum_iY_i(u).
$$
Under a common <hazard function> and <independent censoring>, the conditional event rate is $Y(u)h(u)$. Equivalently, the <counting-process compensator> satisfies $\mathbb E[dN(u)\mid\mathcal F_{u-}]=Y(u)dH(u)$. Estimate a <cumulative hazard> increment by the observed event increment divided by the current <risk set>:
$$
d\widehat H(u)=\frac{dN(u)}{Y(u)}.
$$
With no ties, $dN$ has mass $v_i$ at $x_i$, and $Y(x_i)=\sum_{j:x_j\geq x_i}1$. Thus the <Nelson–Aalen estimator> is
$$
\boxed{\widehat H(t)=\int_0^t\frac{dN(u)}{Y(u)}
=\sum_{i:x_i\leq t}\frac{v_i}{\sum_{j:x_j\geq x_i}1}.}
$$
Only event times contribute, so no empty <risk set> is divided into an event count. <Right-censored> observations contribute time to the <risk sets>, but no event increment.
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