Numerical Analysis of Test Optimality

Philipp Ketz, Adam McCloskey and Jan Scherer

Papers from arXiv.org

Abstract: In nonstandard testing environments, researchers often derive ad hoc tests with correct (asymptotic) size, but their optimality properties are typically unknown a priori and difficult to assess. This paper develops a numerical framework for determining whether an ad hoc test is effectively optimal - approximately maximizing a weighted average power criterion for some weights over the alternative and attaining a power envelope generated by a single weighted average power-maximizing test. Our approach uses nested optimization algorithms to approximate the weight function that makes an ad hoc test's weighted average power as close as possible to that of a true weighted average power-maximizing test, and we show the surprising result that the rejection probabilities corresponding to the latter form an approximate power envelope for the former. We provide convergence guarantees, discuss practical implementation and apply the method to the weak instrument-robust conditional likelihood ratio test and a recently-proposed test for when a nuisance parameter may be on or near its boundary.

Date: 2025-12
References: Add references at CitEc
Citations:

Downloads: (external link)
http://arxiv.org/pdf/2512.19843 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:2512.19843

Access Statistics for this paper

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