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An estimation procedure that is often claimed to be part of Bayesian statistics is the maximum a posteriori (MAP) estimate of an unknown quantity, that equals the mode of the posterior density with respect to some reference measure, typically the Lebesgue measure.
The EM iteration alternates between performing an expectation (E) step, which creates a function for the expectation of the log-likelihood evaluated using the current estimate for the parameters, and a maximization (M) step, which computes parameters maximizing the expected log-likelihood found on the E step. These parameter-estimates are then ...
While the convergence of a method involves investigating how well the numerical approximations match the exact solution, in simplified terms the "reverse" question is asked in the case of consistency: How well does the exact solution fulfill the method specification? In this general theory, a method is convergent if it is consistent and stable.
In statistics, the method of estimating equations is a way of specifying how the parameters of a statistical model should be estimated.This can be thought of as a generalisation of many classical methods—the method of moments, least squares, and maximum likelihood—as well as some recent methods like M-estimators.
In statistics, a generalized estimating equation (GEE) is used to estimate the parameters of a generalized linear model with a possible unmeasured correlation between observations from different timepoints. [1] [2]
For example, a maximum-likelihood estimate is the point where the derivative of the likelihood function with respect to the parameter is zero; thus, a maximum-likelihood estimator is a critical point of the score function. [8] In many applications, such M-estimators can be thought of as estimating characteristics of the population.
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Logically, an estimator is minimax when it is the best in the worst case. Continuing this logic, a minimax estimator should be a Bayes estimator with respect to a least favorable prior distribution of .