Identification of the population target and consistency of the proxy-likelihood estimator

Establish whether the expected score equation for the Hüsler–Reiss composite proxy-likelihood has a unique solution at the target parameter and thereby determine the corresponding consistency properties of the maximum proxy-likelihood estimator.

Background

The paper uses an estimating-equations perspective to motivate the composite-likelihood penalty and sandwich variance estimation. However, the proxy-likelihood is deliberately constructed without specifying the data-generating likelihood, because the target TLETS models have intractable likelihoods.

Consequently, the authors cannot establish that the expected score vanishes uniquely at the true target parameter. This leaves unresolved the population interpretation and formal consistency of the maximum proxy-likelihood estimator.