Universal Inference with Composite Likelihoods

TL;DR

This paper extends the universal inference framework to composite likelihoods, enabling valid multivariate and sequential inference when the full data-generating process is unknown, thus broadening the applicability of split-data likelihood ratio methods.

Contribution

It demonstrates that split-data composite likelihood ratios can be used for universal, finite-sample valid inference, including sequential analysis, when the model is only partially specified.

Findings

Composite likelihood ratios provide valid inference in unknown models.

The approach applies to multivariate and sequential inference scenarios.

It generalizes previous likelihood ratio methods to composite likelihoods.

Abstract

Wasserman et al. (2020, PNAS, vol. 117, pp. 16880-16890) constructed estimator agnostic and finite-sample valid confidence sets and hypothesis tests, using split-data likelihood ratio-based statistics. We demonstrate that the same approach extends to the use of split-data composite likelihood ratios as well, and thus establish universal methods for conducting multivariate inference when the data generating process is only known up to marginal and conditional relationships between the coordinates. Always-valid sequential inference is also considered.