  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.
