Rare clinical outcomes pose a difficulty deeper than ordinary class imbalance: a penalized logistic model can return finite, stable-looking coefficients before the data support a reliable threshold decision. We formulate the accrual question as decision-targeted sequential certification. On a prespecified finite monitoring schedule and target set, asymptotic prediction bands are adjusted for simultaneous coverage, and certification is assessed only among profiles that might be referred, so that a large low-risk majority cannot trigger an uninformative stop. Under the working rare-event logistic model and stated regularity conditions, each certified decision is asymptotically model-conditionally correct with probability at least \(1-\alpha\) over the schedule, and the effective information scales with the number of genuine events. Simulations and a US linked birth/infant-death application illustrate the gap between a model that is merely estimable and one whose decisions are certifiable: the whole-population rule stopped while more than half of referral-relevant profiles remained ambiguous, whereas the decision-targeted rule did not certify by the 300{,}000-birth horizon despite stable temporal validation. Regularization makes a rare-event model estimable but does not substitute for genuine rare-event information.
The \emph{conditional forecast-revision scale} $\It=\{\Var(\E[X_{t+1}\mid\F_t]\mid\F_{t-1})\}^{1/2}$ measures the history-specific size of the forecast update induced by observing $X_t$. Because it is a conditional second moment built from two unknown conditional means, it is not directly observed. We study which estimator of $\It$ should be used under different structural assumptions and computational budgets. The comparison includes a block bootstrap, a conditional-variance model, a fitted state-space model, two $O(1)$ streaming smoothers, and the forget gate of an already-trained recurrent network. An error decomposition separates one-step-prediction error from conditional-second-moment tracking error. We show that externally tuned lag-only smoothers can be inconsistent when $\It$ changes at the sampling scale, although they attain the usual $T^{-2/3}$ mean-squared-error rate ($T^{-1/3}$ for $\It$) under slow variation; a correctly specified state-space estimator escapes this limit by using the current state. In volatility-driven designs, a cheap conditional-variance model is more accurate and over one hundred times cheaper \emph{as a point estimator} than the implemented block bootstrap, whose value lies in the sampling distribution it provides rather than in point tracking. In state-driven designs, only the structurally matched filter recovers the fast variation. Read directly, a trained network's forget gate does not track $\It$ --- though a supervised linear probe on the full gate vector does, so $\It$ is linearly decodable but not available for free. These results yield a practical rule: identify the conditional-second-moment structure, match the estimator to it, and then choose the least costly adequate method.
H. Foo, Y. Chang· 0 citations
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