Paper Overview
- Field: Machine Learning
- Author: Pedro Cadahia Delgado
- Published: 2026-08-21
- arXiv: 2608.21334
Summary
Short observational pricing panels can contain many observations while offering only a small number of distinct price movements. This paper studies the inferential consequences of that distinction in a synthetic data-generating process calibrated to a sparse pricing regime. The author separates uncertainty conditional on a realized price trajectory from variation in estimation error across alternative trajectories generated by the same pricing process. In the baseline simulations, the latter component accounts for 97.6% of the variance of estimation error for the gradient-boosted specification. Within-panel resampling procedures use the information of one realized trajectory and do not identify this across-design component.
Key Findings
1. Empirical dispersion law: Across-design dispersion is well described by the empirical relation
sigma_hat ≈ 0.182 V^(-0.271)
where V equals the number of moves multiplied by amplitude squared.
2. Shared price paths do not add independent variation: Adding regions that share a common price path reduces outcome noise but does not create independent price trajectories. Instead, averaging over units with independent design-specific errors reduces dispersion at the standard square-root rate.
3. Paule-Mandel variance components improve coverage: Variance components estimated across independent pricing units via the Paule-Mandel method substantially improve empirical coverage in uniform simulations, rising from 0.469 to 0.931.
Implications
The broader implication is a shift toward data-generating processes that create independent identification variation, rather than relying solely on fixed passive panels. Standard resampling within a single realized trajectory understates uncertainty when pricing is sparse, since most estimation-error variance originates across alternative designs rather than within the observed one.