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The EM algorithm consists of two steps: the E-step and the M-step. Firstly, the model parameters and the () can be randomly initialized. In the E-step, the algorithm tries to guess the value of () based on the parameters, while in the M-step, the algorithm updates the value of the model parameters based on the guess of () of the E-step.
In econometrics and statistics, the generalized method of moments (GMM) is a generic method for estimating parameters in statistical models.Usually it is applied in the context of semiparametric models, where the parameter of interest is finite-dimensional, whereas the full shape of the data's distribution function may not be known, and therefore maximum likelihood estimation is not applicable.
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.
In econometrics, the Arellano–Bond estimator is a generalized method of moments estimator used to estimate dynamic models of panel data.It was proposed in 1991 by Manuel Arellano and Stephen Bond, [1] based on the earlier work by Alok Bhargava and John Denis Sargan in 1983, for addressing certain endogeneity problems. [2]
In statistics, generalized least squares (GLS) is a method used to estimate the unknown parameters in a linear regression model.It is used when there is a non-zero amount of correlation between the residuals in the regression model.
The estimator can be derived in terms of the generalized method of moments (GMM). Also often discussed in the literature (including White's paper) is the covariance matrix Ω ^ n {\displaystyle {\widehat {\mathbf {\Omega } }}_{n}} of the n {\displaystyle {\sqrt {n}}} -consistent limiting distribution:
A typical finite-dimensional mixture model is a hierarchical model consisting of the following components: . N random variables that are observed, each distributed according to a mixture of K components, with the components belonging to the same parametric family of distributions (e.g., all normal, all Zipfian, etc.) but with different parameters
The identification conditions require that the system of linear equations be solvable for the unknown parameters.. More specifically, the order condition, a necessary condition for identification, is that for each equation k i + n i ≤ k, which can be phrased as “the number of excluded exogenous variables is greater or equal to the number of included endogenous variables”.