Target-Aware Sequential Inference: Pooled versus Stratified Anytime-Valid Designs
Abstract
Sequential studies with heterogeneous strata may define the estimand under a target mixture that differs from the sampling distribution. We organize the design problem by guarantee class: one pooled confidence sequence for a single prespecified target, shared pooled inference for a prespecified target set, and stratum-resolved inference when local guarantees must remain available. For target-set pooled inference we derive minimax, gap-aware, and range-capped shared proposals and an adaptive tracking rule. A specialized augmented off-policy score removes between-stratum mean heterogeneity asymptotically, recovering Neyman allocation for efficient single-target pooled inference. Robust directional certification over a convex target set is a classical intersection-union problem and does not require an M-fold vertex split. We derive a Gaussian information lower bound and an exact finite-support characteristic information that coincides with the bounded nonparametric KL-inf limit, and state sufficient conditions for first-order attainment of the Gaussian constant. Within the local-CS architecture, regularly varying boundaries imply a general allocation law with the 2/3 exponent for root-n variance-adaptive widths. Simulations and a PromptEval replay illustrate the resulting guarantee-efficiency frontier.
Related
- A Tutorial on Safe Anytime-Valid Inference: Practical Maximally Flexible Sampling Designs for Experiments Based on e-Values
- Anytime-Valid Inference in Linear Models with Applications to Regression-Adjusted Causal Inference
- Asymptotic Anytime-Valid Quantile Inference under Local Differential Privacy
- Anytime-Valid Inference in Conjoint Experiments
- Moment-Orthogonal Quadratic-Envelope E-Processes for Anytime-Valid Location Inference
BibTeX
@misc{hait2026targetaware,
title = {{Target-Aware Sequential Inference: Pooled versus Stratified Anytime-Valid Designs}},
author = {Subir Hait},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.37873},
eprint = {2609.37873},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37873},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Target-Aware Sequential Inference: Pooled versus Stratified Anytime-Valid Designs
AU - Subir Hait
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2609.37873
UR - https://arxiv.org/abs/2609.37873
AB - Sequential studies with heterogeneous strata may define the estimand under a target mixture that differs from the sampling distribution. We organize the design problem by guarantee class: one pooled confidence sequence for a single prespecified target, shared pooled inference for a prespecified target set, and stratum-resolved inference when local guarantees must remain available. For target-set pooled inference we derive minimax, gap-aware, and range-capped shared proposals and an adaptive tracking rule. A specialized augmented off-policy score removes between-stratum mean heterogeneity asymptotically, recovering Neyman allocation for efficient single-target pooled inference. Robust directional certification over a convex target set is a classical intersection-union problem and does not require an M-fold vertex split. We derive a Gaussian information lower bound and an exact finite-support characteristic information that coincides with the bounded nonparametric KL-inf limit, and state sufficient conditions for first-order attainment of the Gaussian constant. Within the local-CS architecture, regularly varying boundaries imply a general allocation law with the 2/3 exponent for root-n variance-adaptive widths. Simulations and a PromptEval replay illustrate the resulting guarantee-efficiency frontier.
ER -