Rajen Shah | Searcharxiv

arXiv2026

Aggregation of Statistical Evidence under Exchangeability

We study aggregation of statistical evidence under unknown and potentially complex dependence using group-invariance. Building on permutation-based constructions that treat transformed datasets as exchangeable units, we aggregate evidence across statistics for each transformed dataset and calibrate the resulting aggregates across transformations. We develop a finite-sample power and adaptivity theory for this framework, together with extensions to sequential and data-dependent aggregation that preserve validity. For single-batch aggregation, which uses one collection of transformed datasets for both standardization and calibration, we show that the critical values uniformly improve on deterministic calibrations valid under arbitrary dependence, including Bonferroni correction, while adapting to the unknown dependence structure. We also introduce a sequential alpha-spending version that permits early rejection when evidence is strong, and a two-batch extension that separates standardization from calibration to accommodate learned aggregation rules and reduce computation. Applications to adaptive nonparametric testing and conformal prediction illustrate how these results sharpen existing aggregation methods.

stat.ME↗

arXiv2025

Latent confounding in high-dimensional nonlinear models

We consider the the problem of identifying causal effects given a high-dimensional treatment vector in the presence of low-dimensional latent confounders. We assume a parametric structural causal model in which the outcome is permitted to depend on a sparse linear combination of the treatment vector and confounders nonlinearly. We consider a generalisation of the LAVA estimator of Chernozhukov et al. [2017] for estimating the treatment effects and show that under the so-called `dense confounding' assumption that each confounder can affect a wide range of observed treatment variables, one can estimate the causal parameters at the same rate as possible without confounding. Notably, the results permit a form of weak confounding in that the minimum non-zero singular value of the loading matrix of the confounders can grow more slowly than the $\sqrt{p}$, where $p$ is the dimension of the treatment vector. We further use our generalised LAVA procedure within a generalised covariance measure-based test for edges in a causal DAG in the presence of latent confounding.

math.ST↗