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

Karun Adusumilli

Papers from arXiv.org

Abstract: The aim of this paper is to develop techniques for incorporating the cost of information into experimental design. Specifically, 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 to 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 the diffusion limit, we describe the optimal policies under the minimax regret criterion. Under small cost asymptotics, the same policies are also optimal under parametric and non-parametric distributions of outcomes. The minimax optimal sampling rule is just the Neyman allocation; it is independent of sampling costs and does not adapt to previous outcomes. The decision-maker stops sampling when the average difference between the treatment outcomes, multiplied by the number of observations collected until that point, exceeds a specific threshold. The results derived here also apply to best arm identification with two arms.

Date: 2022-10, Revised 2024-02
New Economics Papers: this item is included in nep-exp
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://arxiv.org/pdf/2210.15841 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2210.15841

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().