= Score and information of Cox partial likelihood
{title2=$U(\beta)=\sum_j[z_{i_j}-\bar z_j(\beta)],\quad I(\beta)=\sum_j\operatorname{Cov}_{w_j}(z)$}
At an untied event time, the <Cox partial likelihood> weights the current <risk set> by $w_{jk}=e^{\beta^Tz_k}/\sum_{\ell\in R_j}e^{\beta^Tz_\ell}$. Differentiation gives the displayed <score function> and the negative Hessian as a sum of weighted covariances. The score is the sum of <Schoenfeld functions>, so <Schoenfeld residuals> sum to zero at a finite interior unpenalized fit. At arbitrary trial coefficients or boundary fits, a zero sum is not a general identity.
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