In statistics a quasi-maximum likelihood estimate (QMLE), also known as a pseudo-likelihood estimate or a composite likelihood estimate, is an estimate of a parameter θ in a statistical model that is formed by maximizing a function that is related to the logarithm of the likelihood function, but in discussing the consistency and (asymptotic) variance-covariance matrix, we assume some parts of the distribution may be mis-specified.
Doing this only makes sense if the dependency structure is a nuisance parameter with respect to the goals of the analysis.
[3] As long as the quasi-likelihood function that is maximized is not oversimplified, the QMLE (or composite likelihood estimate) is consistent and asymptotically normal.
It is less efficient than the maximum likelihood estimate, but may only be slightly less efficient if the quasi-likelihood is constructed so as to minimize the loss of information relative to the actual likelihood.
[4] Standard approaches to statistical inference that are used with maximum likelihood estimates, such as the formation of confidence intervals, and statistics for model comparison,[5] can be generalized to the quasi-maximum likelihood setting.