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Maximum likelihood estimation

Allow for non-normal counts, typically Poisson/binomial/neg. binomial. Still assumes measurement error only (no process error). Generalized least-squares achieves a similar goal.

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Maximum likelihood estimation
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If the likelihood function (the prob. model) is correctly specified
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Expectation-maximization (EM)
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Household models
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Least-squares fitting
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Methods incorporating both process and observation error
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Sensitive to model misspecification
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