Towards unifying second-order theory of likelihoods and pseudolikelihoods

Theory is developed to show that second-order distributional behaviour of pseudolikelihood ratios can be modified to resemble that of likelihood counterparts by means of a suitable adjustment. The latter is conceived to enable the Bartlett correction for pseudolikelihood ratios when inference focuses on a scalar parameter. The proposed methodology can be framed in the likelihood setting where it can be interpreted as a device to achieve secondorder accurate inference that takes into an account potential erroneous model assumptions. The efficacy of the proposal is demonstrated via simulation studies.