Confidence sequences with composite likelihoods

In dominated parametric statistical models, confidence sequences provide conservatively valid frequentist inference directly from a likelihood ratio. They ensure a specific mode of replicability when inference is performed on accumulating data: inferential conclusions that are compatible with a guaranteed probability when the sample is enlarged, in the form of overlapping confidence regions. Here we consider both Robbins' mixture confidence sequences and running maximum likelihood confidence sequences recently considered by Wasserman, Ramdas, and Balakrishnan. We compare through simulation the replicability properties of the two kinds of confidence sequences, evaluating, along a prospected enlargement of the sample, the frequency of incompatible estimation intervals and the frequency of failure of simultaneous coverage of the true parameter value. Moreover, we propose a shortcut to extend the application of mixture confidence sequences to pseudo-likelihoods, in particular to composite likelihood. The main assumption required is that normal asymptotic theory offers a good approximation to the density of the maximizer of the pseudo-likelihood. When inference is about a scalar parameter of interest, the computation of the proposed sequence of confidence intervals is straightforward. The method is illustrated by an example with replicability properties evaluated through simulation.