Infinite Diameter Confidence Sets in Hedges' Publication Bias Model

TL;DR

This paper demonstrates that in Hedges' publication bias model, it is impossible to construct confidence sets with guaranteed finite diameter, explaining the inference difficulties in such models.

Contribution

The paper proves a fundamental limitation in constructing finite confidence sets for Hedges' selection model using a generalized Gleser-Hwang theorem.

Findings

No confidence set of guaranteed finite diameter exists for Hedges' model parameters.

Provides theoretical explanation for inference challenges in publication bias models.

Highlights limitations of current statistical methods in meta-analysis with publication bias.

Abstract

Meta-analysis, the statistical analysis of results from separate studies, is a fundamental building block of science. But the assumptions of classical meta-analysis models are not satisfied whenever publication bias is present, which causes inconsistent parameter estimates. Hedges' selection function model takes publication bias into account, but estimating and inferring with this model is tough for some datasets. Using a generalized Gleser-Hwang theorem, we show there is no confidence set of guaranteed finite diameter for the parameters of Hedges' selection model. This result provides a partial explanation for why inference with Hedges' selection model is fraught with difficulties.