Maximum Sample Likelihood
Maximum sample likelihood is a method for fitting a distribution to a complex survey sample.
Compare to maximum pseudo-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.
This method maximizes sample likelihood instead, and uses this as an estimator for the population likelihood