Conditional validity of prediction-powered inference for spatially dependent finite populations
Abstract
Prediction-powered inference (PPI) combines full-frame predictions with a small labelled sample to estimate finite-population regression coefficients. We establish conditions for the conditional validity of existing calibrated residual-regression PPI estimators under nonuniform label acquisition and spatially dependent prediction errors. Approximate calibration can leave a population-specific displacement: the projection of prediction errors onto coefficient-specific calibration defects. We characterize its role in conditional inference through the noncentrality of a fixed-candidate Wald region. The relevant target-weight function is the coefficient loading divided by acquisition intensity. When mean-approximation error does not dominate, directional covariance control yields a wider sufficient recovery regime than a total residual-energy bound. A bounded spectral-basis theorem gives conditional coverage under directional covariance, tail and nondegeneracy conditions, with Gaussian and bounded non-Gaussian spatial examples. The analysis accounts for estimation of the one-step augmentation and permits same-label selection from a fixed finite library with a common first-order influence vector. A periodic Fourier construction attains the stochastic directional-gap order within a restricted dictionary class. Constructed and real-record-set experiments illustrate why mean calibration need not protect a slope. The results concern descriptive census projection coefficients under the stated sampling and field conditions.
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BibTeX
@misc{shirota2026conditional,
title = {{Conditional validity of prediction-powered inference for spatially dependent finite populations}},
author = {Shinichiro Shirota},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.10356},
eprint = {2608.10356},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.10356},
}
RIS
TY - UNPB
TI - Conditional validity of prediction-powered inference for spatially dependent finite populations
AU - Shinichiro Shirota
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2608.10356
UR - https://arxiv.org/abs/2608.10356
AB - Prediction-powered inference (PPI) combines full-frame predictions with a small labelled sample to estimate finite-population regression coefficients. We establish conditions for the conditional validity of existing calibrated residual-regression PPI estimators under nonuniform label acquisition and spatially dependent prediction errors. Approximate calibration can leave a population-specific displacement: the projection of prediction errors onto coefficient-specific calibration defects. We characterize its role in conditional inference through the noncentrality of a fixed-candidate Wald region. The relevant target-weight function is the coefficient loading divided by acquisition intensity. When mean-approximation error does not dominate, directional covariance control yields a wider sufficient recovery regime than a total residual-energy bound. A bounded spectral-basis theorem gives conditional coverage under directional covariance, tail and nondegeneracy conditions, with Gaussian and bounded non-Gaussian spatial examples. The analysis accounts for estimation of the one-step augmentation and permits same-label selection from a fixed finite library with a common first-order influence vector. A periodic Fourier construction attains the stochastic directional-gap order within a restricted dictionary class. Constructed and real-record-set experiments illustrate why mean calibration need not protect a slope. The results concern descriptive census projection coefficients under the stated sampling and field conditions.
ER -