# Bregman projection for calibration estimation in Survey Sampling

arXiv: https://arxiv.org/abs/2603.20780 · HTML: https://mlsanity.com/paper/2603.20780/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Mar 2026.

## Built on by (most cited first, 1 of 1)

- [MEC-Cox: Machine-Learning-Assisted Generalized Entropy Calibration for ATT Marginal Hazard-Ratio Estimation](https://mlsanity.com/paper/2606.08305/) (2026)

## Abstract (arXiv)

Calibration weighting is a fundamental tool in survey sampling for incorporating auxiliary population information into design-based estimators. Classical formulations measure distance between calibrated and design weights on the multiplicative ratio scale. We develop a unified framework based on Bregman divergence defined directly on the weight vector. The framework reveals a primal--dual symmetry in which both the weight-space and multiplier-space optimization problems are themselves Bregman projections, and the calibrated weights satisfy a generalized Pythagorean decomposition with respect to the constraint manifold. The resulting estimator is asymptotically equivalent to a debiased prediction estimator whose regression coefficient depends explicitly on the Bregman generator, in contrast to the generalized regression estimator equivalent of classical calibration. Exploiting this dependence, we identify a contrast-entropy generator that achieves design-optimality under Poisson sampling. Two extensions are developed: cross-fitted estimation under non-probability sampling, yielding doubly robust inference under standard product-rate conditions; and a regularized extension whose Lagrangian dual produces a H"older-conjugate penalty for soft balance under high-dimensional auxiliary variables. Simulations and an analysis of National Oceanic and Atmospheric Administration (NOAA)'s Large Pelagics Intercept Survey illustrate the framework.