K. C. Gary Chan | Searcharxiv

arXiv2026

The Categorical Instrumental Variable Model: Characterization, Partial Identification, and Statistical Inference

We study categorical instrumental variable (IV) models with instrument, treatment and outcome taking finitely many values. We derive a simple closed-form characterization of the set of joint distributions of potential outcomes that are compatible with a given observed data distribution in terms of a minimal set of inequalities. These inequalities unify several different IV models defined by versions of the independence and exclusion restriction assumptions. They lead to sharp bounds on causal functionals and provide a sharp criterion for model falsification. For linear functionals of the joint counterfactual distribution, such as pairwise average treatment effects and probabilities of potential outcomes, we construct confidence intervals with simultaneous finite-sample coverage, using a tail bound on the Kullback--Leibler divergence. We illustrate our method using data from the Minneapolis Domestic Violence Experiment.

math.ST↗

arXiv2026

Robust and Efficient Semiparametric Inference for the Stepped Wedge Design

Stepped wedge designs (SWDs) are increasingly used to evaluate longitudinal cluster-level interventions but pose substantial challenges for valid inference. Because crossover times are randomized, intervention effects are intrinsically confounded with secular time trends, while heterogeneity across clusters, complex correlation structures, baseline covariate imbalances, and small numbers of clusters further complicate inference. We propose a unified semiparametric framework for estimating possibly time-varying intervention effects in SWDs. Under a semiparametric model on treatment contrast, we develop a nonstandard semiparametric efficiency theory that accommodates correlated observations within clusters, varying cluster-period sizes, and weakly dependent treatment assignments. The resulting estimator is consistent and asymptotically normal even under misspecified covariance structure and control cluster-period means, and is efficient when both are correctly specified. To enable inference with few clusters, we exploit the permutation structure of treatment assignment to propose a standard error estimator that reflects finite-sample variability, with a leave-one-out correction to reduce plug-in bias. The framework also allows incorporation of effect modification and adjustment for imbalanced precision variables through design-based adjustment or double adjustment that additionally incorporates an outcome-based component. Simulations and application to a public health trial demonstrate the robustness and efficiency of the proposed method relative to standard approaches.

stat.ME↗