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Optimal Stratified Allocation for Rare-Event Onset Forecasting in Dependent Sequences

arXiv · AI, language, vision and robotics · article · Sep 3, 2026 · UTC

Let a finite population of n labelled examples carry a class-weighted loss, with pi*n in a rare positive class weighted by N0/N1. We study estimation of total risk from a subsample K << n under designs allocating K0 and K1 draws to the two strata. We derive the exact finite-population variance of the weighted risk estimator under class-conditional sampling without replacement and solve for the optimal allocation. The class multiplier inflates positive-stratum dispersion by the imbalance ratio, causing that ratio to cancel from the optimal allocation and making equal, rather than proportional,

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