Maximum Pseudo-likelihood
Maximum pseudo-likelihood (or pseudo-maximum likelihood) is a method for fitting a distribution to an estimated population.
Compare to maximum sample likelihood.
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Description
The naive extension of MLE to a weighted sample is to calculate the weighted sum of log likelihoods. But strictly speaking, since a complex survey sample is weighted and/or not independently distributed, it is insufficient to define the likelihood function in terms of the model parameters and the observations. Technically the likelihood of the model should be maximized given the observations and the measurements used to design the sample. However, it is clearly true that MLE is consistent if the entire population is surveyed (i.e., a census)
This method maximizes pseudo-likelihood given the estimated population.