However, sampling is not the only source of uncertainty. In practice, distributions change between locations and across time.

Local treatment effects are a common quantity found throughout the empirical sciences that measure the treatment effect among those who comply with what they are assigned. Most of the literature is focused on estimating the average of such quantity, which is called the " local average treatment effect (LATE) " [

We study nonasymptotic (finite-sample) confidence intervals for treatment effects in randomized experiments. In the existing literature, the effective sample sizes of nonasymptotic confidence intervals tend to be looser than the corresponding central-limit-theorem-based confidence intervals by a factor depending on the square root of the propensity score. We show that this performance gap can be closed, designing nonasymptotic confidence intervals that have the same effective sample size as their asymptotic counterparts. Our approach involves systematic exploitation of negative dependence or variance adaptivity (or both). We also show that the nonasymptotic rates that we achieve are unimprovable in an information-theoretic sense.

Investigating the marginal causal effect of an intervention on an outcome from complex data remains challenging due to the inflexibility of employed models and the lack of complexity in causal benchmark datasets, which often fail to reproduce intricate real-world data patterns. In this paper we introduce Frugal Flows, a likelihood-based machine learning model that uses normalising flows to flexibly learn the data-generating process, while also directly targeting the marginal causal quantities inferred from observational data. We provide a novel algorithm for fitting a model to observational data with a parametrically specified causal distribution, and propose that these models are exceptionally well suited for synthetic data generation to validate causal methods. Unlike existing data generation methods, Frugal Flows generate synthetic data that closely resembles the empirical dataset, while also automatically and exactly satisfying a user-defined average treatment effect. To our knowledge, Frugal Flows are the first generative model to both learn flexible data representations and also \textit{exactly} parameterise quantities such as the average treatment effect and the degree of unobserved confounding. We demonstrate the above with experiments on both simulated and real-world datasets.

The design of efficient nonparametric estimators has long been a central problem in statistics, machine learning, and decision making. Classical optimal procedures often rely on strong structural assumptions, which can be misspecified in practice and complicate deployment. This limitation has sparked growing interest in structure-agnostic approaches -- methods that debias black-box nuisance estimates without imposing structural priors. Understanding the fundamental limits of these methods is therefore crucial. This paper provides a systematic investigation of the optimal error rates achievable by structure-agnostic estimators. We first show that, for estimating the average treatment effect (ATE), a central parameter in causal inference, doubly robust learning attains optimal structure-agnostic error rates. We then extend our analysis to a general class of functionals that depend on unknown nuisance functions and establish the structure-agnostic optimality of debiased/double machine learning (DML). We distinguish two regimes -- one where double robustness is attainable and one where it is not -- leading to different optimal rates for first-order debiasing, and show that DML is optimal in both regimes. Finally, we instantiate our general lower bounds by deriving explicit optimal rates that recover existing results and extend to additional estimands of interest. Our results provide theoretical validation for widely used first-order debiasing methods and guidance for practitioners seeking optimal approaches in the absence of structural assumptions. This paper generalizes and subsumes the ATE lower bound established in \citet{jin2024structure} by the same authors.

Firms often develop targeting policies to personalize marketing actions and improve incremental profits. Effective targeting depends on accurately separating customers with positive versus negative treatment effects. We propose an approach to estimate the conditional average treatment effects (CATEs) of marketing actions that aligns their estimation with the firm's profit objective. The method recognizes that, for many customers, treatment effects are so extreme that additional accuracy is unlikely to change the recommended actions. However, accuracy matters near the decision boundary, as small errors can alter targeting decisions. By modifying the firm's objective function in the standard profit maximization problem, our method yields a near-optimal targeting policy while simultaneously estimating CATEs. This introduces a new perspective on CATE estimation, reframing it as a problem of profit optimization rather than prediction accuracy. We establish the theoretical properties of the proposed method and demonstrate its performance and trade-offs using synthetic data.

Observational data is widely utilized when randomized experiments are infeasible or fail to adequately represent target populations. A key challenge in observational analysis is the lack of overlap between treatment and control groups. Even when a nominally large dataset is collected, the effective sample size may be prohibitively small when there is a region with little overlap between treated and control populations. As an example, if the treatment of interest is rarely observed among older citizens, estimating their counterfactual (treated) outcome becomes inherently unreliable. This challenge is further exacerbated in modern operational contexts, where high-dimensional covariate representations [15] increase data sparsity, making causal identification particularly difficult in regions of the covariate space with small effective sample size.