A note on pseudolikelihood constructed from marginal densities

For likelihood-based inference involving distributions in which high-dimensional dependencies are present it may be useful to use approximate likelihoods based, for example, on the univariate or bivariate marginal distributions. The asymptotic properties of formal maximum likelihood estimators in such cases are outlined. In particular, applications in which only a single q x 1 vector of observations is observed are examined. Conditions under which consistent estimators of parameters result from the approximate likelihood using only pairwise joint distributions are studied. Some examples are analysed in detail.