Sharp Fréchet--Hoeffding Bounds under Selectively Incomplete Observation

Rami V. Tabri

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arXiv · 2611.03075

Sharp Fréchet--Hoeffding Bounds under Selectively Incomplete Observation

Rami V. Tabri

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Abstract

Incomplete records can sharpen bounds on joint outcome probabilities even when no pair of outcomes is jointly observed. I derive sharp pointwise Fréchet--Hoeffding bounds combining known population marginals with selectively observed records, without restricting the observation mechanism. I establish an exact reduction of the identification problem to finite-dimensional optimization, yielding computable characterizations of both bounds. Illustrations involving income mobility, potential outcomes, and split questionnaires demonstrate how incomplete records can improve identification relative to the classical bounds.

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Rami V. Tabri. 2026-11-02. Sharp Fréchet--Hoeffding Bounds under Selectively Incomplete Observation. https://arxiv.org/abs/2611.03075

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