How to sample and when to stop sampling: The generalized Wald problem and minimax policies

Karun Adusumilli

Home/Archive/arXiv

arXiv · 2210.15841

How to sample and when to stop sampling: The generalized Wald problem and minimax policies

Karun Adusumilli

View original source ↗Read source document ↗Export metadata ↓

Abstract

We study sequential experiments where sampling is costly and a decision-maker aims to determine the best treatment for full scale implementation by (1) adaptively allocating units between two possible treatments, and (2) stopping the experiment when the expected welfare (inclusive of sampling costs) from implementing the chosen treatment is maximized. Working under a continuous time limit, we characterize the optimal policies under the minimax regret criterion. We show that the same policies also remain optimal under both parametric and non-parametric outcome distributions in an asymptotic regime where sampling costs approach zero. The minimax optimal sampling rule is just the Neyman allocation: it is independent of sampling costs and does not adapt to observed outcomes. The decision-maker halts sampling when the product of the average treatment difference and the number of observations surpasses a specific threshold. The results derived also apply to the so-called best-arm identification problem, where the number of observations is exogenously specified.

Explore related subjects

econ.EM

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Karun Adusumilli. 2025-05-03. How to sample and when to stop sampling: The generalized Wald problem and minimax policies. https://arxiv.org/abs/2210.15841

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Poverty Targeting with Imperfect Information

How should antipoverty programs allocate transfers when household income is known only through noisy predictions? I formulate this as a statistical decision problem in which a policymaker chooses nonnegative transfers within a fixed budget to minimize squared deviations of post-transfer income from the poverty line. I show that the standard plug-in rule, which treats predictions as exact, is inadmissible. I then develop a nonparametric empirical Bayes allocation rule that replaces the estimated gaps with posterior mean poverty gaps. Its Bayes regret is bounded by the mean squared difference between its posterior mean gaps and the oracle's, so the budget and nonnegativity constraints do not slow its convergence to the oracle. The approach extends, with weaker guarantees, to a planner who cares only about how far households remain below the poverty line after transfers and to programs that pay a fixed set of benefit amounts. In simulations using household surveys from nine African countries, the allocations under the empirical Bayes rule reach about 1.8 times as many poor people as those under plug-in OLS with the same budget and achieve the same average poverty gap reduction with 6.7% less spending.

econ.EM↗

arXiv2026

Estimating Treatment Effects in Panel Data Without Parallel Trends

This paper proposes a novel approach for estimating treatment effects in panel data settings, addressing key limitations of the standard difference-in-differences (DID) approach. The standard approach relies on the parallel trends assumption, implicitly requiring that unobservable factors correlated with treatment assignment be unidimensional, time-invariant, and affect untreated potential outcomes in an additively separable manner. This paper introduces a more flexible framework that allows for multidimensional unobservables and non-additive separability, and provides sufficient conditions for identifying the average treatment effect on the treated. An empirical application to job displacement reveals substantially smaller long-run earnings losses compared to the standard DID approach, demonstrating the framework's ability to account for unobserved heterogeneity that manifests as differential outcome trajectories between treated and control groups.

econ.EM↗

arXiv2026

Single-Network Finite-Sample Inference in Strategic Network Formation Models

We develop a finite-sample valid inference procedure for strategic network formation models with endogenous network statistics, using only a single observed network. We impose no restrictions on network density, equilibrium selection, or the dependence structure induced by strategic interaction. Using a "bounding-by-c" technique, we obtain realization-wise sandwich inequalities whose middle term depends only on exogenous covariates and i.i.d. pairwise shocks. These inequalities deliver pathwise identifying restrictions and simulable finite-sample critical values in both parametric and semiparametric settings. Our proposed procedure is also computationally tractable: it does not involve solving, simulating, or enumerating equilibrium (sub)networks, and easily scales to networks with 10000 agents in simulations. In two empirical applications, we find statistical evidence for positive link interdependence at the 95% confidence level.

econ.EM↗