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In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data.This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable.
For maximum likelihood estimation, the existence of a global maximum of the likelihood function is of the utmost importance. By the extreme value theorem, it suffices that the likelihood function is continuous on a compact parameter space for the maximum likelihood estimator to exist. [7]
Combining the likelihood principle with the law of likelihood yields the consequence that the parameter value which maximizes the likelihood function is the value which is most strongly supported by the evidence. This is the basis for the widely used method of maximum likelihood.
In statistics, an expectation–maximization (EM) algorithm is an iterative method to find (local) maximum likelihood or maximum a posteriori (MAP) estimates of parameters in statistical models, where the model depends on unobserved latent variables. [1]
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.
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 ...
In 1928, Fisher was the first to use diffusion equations to attempt to calculate the distribution of allele frequencies and the estimation of genetic linkage by maximum likelihood methods among populations. [57] In 1930, The Genetical Theory of Natural Selection was first published by Clarendon Press and is dedicated to Leonard Darwin.
The two-step estimator discussed above is a limited information maximum likelihood (LIML) estimator. In asymptotic theory and in finite samples as demonstrated by Monte Carlo simulations, the full information (FIML) estimator exhibits better statistical properties. However, the FIML estimator is more computationally difficult to implement. [9]