RCShift: Certifying When Partial Linkage Suffices for Finite-Sample Decisions
TL;DR
This work introduces RCShift, which certifies two routes to sufficiency under a declared observation contract, and exact mode characterizes minimum-cost family-exact storage through LR-visible cycle directions through LR-visible cycle directions.
Abstract
Systems with costly gold outcomes and cheaper auxiliary observations must decide how much record linkage to retain. Complete pairing retains every joint counter, while separate margins retain none. Neither endpoint is calibrated to a declared finite-sample decision. Universal reconstruction can retain cycle directions invisible to the likelihood-ratio family. Family-exact storage can exceed what the decision requires because certified residual loss may fit within finite-sample slack. We introduce RCShift, which certifies two routes to sufficiency under a declared observation contract. Its exact mode characterizes minimum-cost family-exact storage through LR-visible cycle directions. Its approximate mode bounds reverse Le Cam deficiency. Its integer mode certifies whether a chosen set preserves the full experiment's minimum integer record count at specified size and power. In a rank-two witness, one aligned counter preserves a four-record minimum. An equal-cost misaligned counter and the margins require eleven records, while universal reconstruction requires two counters. A local perturbation has positive reverse deficiency yet retains the four-record minimum. Proof-checked scheduling bounds instantiate the contract before gold computation and yield exact reconstruction on the admitted tree support. RCShift turns partial-linkage storage into decision-calibrated measurement design for the declared family, costs, target, and common strictly positive support.
