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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 logistic regression, the measure of goodness-of-fit is the likelihood function L, or its logarithm, the log-likelihood ℓ. The likelihood function L is analogous to the ε 2 {\displaystyle \varepsilon ^{2}} in the linear regression case, except that the likelihood is maximized rather than minimized.
IRLS is used to find the maximum likelihood estimates of a generalized linear model, and in robust regression to find an M-estimator, as a way of mitigating the influence of outliers in an otherwise normally-distributed data set, for example, by minimizing the least absolute errors rather than the least square errors.
Generalized linear models were formulated by John Nelder and Robert Wedderburn as a way of unifying various other statistical models, including linear regression, logistic regression and Poisson regression. [1] They proposed an iteratively reweighted least squares method for maximum likelihood estimation (MLE) of the model parameters. MLE ...
The method of least squares is a prototypical M-estimator, since the estimator is defined as a minimum of the sum of squares of the residuals.. Another popular M-estimator is maximum-likelihood estimation.
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]
Spreadsheets, web-page calculators, and SAS shouldn't have any problem doing an exact test on a sample size of 1 000 . — John H. McDonald [ 2 ] G -tests have been recommended at least since the 1981 edition of Biometry , a statistics textbook by Robert R. Sokal and F. James Rohlf .
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 ]