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  2. Maximum likelihood estimation - Wikipedia

    en.wikipedia.org/wiki/Maximum_likelihood_estimation

    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.

  3. Scoring algorithm - Wikipedia

    en.wikipedia.org/wiki/Scoring_algorithm

    Scoring algorithm, also known as Fisher's scoring, [1] is a form of Newton's method used in statistics to solve maximum likelihood equations numerically, named after Ronald Fisher. Sketch of derivation

  4. M-estimator - Wikipedia

    en.wikipedia.org/wiki/M-estimator

    For example, in estimating SUR model of 6 equations with 5 explanatory variables in each equation by Maximum Likelihood, the number of parameters declines from 51 to 30. [ 9 ] Despite its appealing feature in computation, concentrating parameters is of limited use in deriving asymptotic properties of M-estimator. [ 10 ]

  5. Estimating equations - Wikipedia

    en.wikipedia.org/wiki/Estimating_equations

    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 .

  6. Expectation–maximization algorithm - Wikipedia

    en.wikipedia.org/wiki/Expectation–maximization...

    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 ...

  7. Iteratively reweighted least squares - Wikipedia

    en.wikipedia.org/wiki/Iteratively_reweighted...

    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.

  8. Two-step M-estimator - Wikipedia

    en.wikipedia.org/wiki/Two-step_M-estimator

    When the first step is a maximum likelihood estimator, under some assumptions, two-step M-estimator is more asymptotically efficient (i.e. has smaller asymptotic variance) than M-estimator with known first-step parameter. Consistency and asymptotic normality of the estimator follows from the general result on two-step M-estimators. [4] Let {V i ...

  9. Baum–Welch algorithm - Wikipedia

    en.wikipedia.org/wiki/Baum–Welch_algorithm

    The Baum–Welch algorithm uses the well known EM algorithm to find the maximum likelihood estimate of the parameters of a hidden Markov model given a set of observed feature vectors. Let X t {\displaystyle X_{t}} be a discrete hidden random variable with N {\displaystyle N} possible values (i.e.