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Model selection is the task of selecting a model from among various candidates on the basis of performance criterion to choose the best one. [1] In the context of machine learning and more generally statistical analysis , this may be the selection of a statistical model from a set of candidate models, given data.
Unlike most other model selection strategies, like the Akaike information criterion (AIC), the Bayesian information criterion (BIC) and the deviance information criterion (DIC), the FIC does not attempt to assess the overall fit of candidate models but focuses attention directly on the parameter of primary interest with the statistical analysis ...
Heckman's correction involves a normality assumption, provides a test for sample selection bias and formula for bias corrected model. Suppose that a researcher wants to estimate the determinants of wage offers, but has access to wage observations for only those who work.
In general, if the goal is prediction, AIC and leave-one-out cross-validations are preferred. If the goal is selection, inference, or interpretation, BIC or leave-many-out cross-validations are preferred. A comprehensive overview of AIC and other popular model selection methods is given by Ding et al. (2018) [30]
The BIC is formally defined as [3] [a] = (^). where ^ = the maximized value of the likelihood function of the model , i.e. ^ = (^,), where {^} are the parameter values that maximize the likelihood function and is the observed data;
They are a popular alternative to the likelihood-based generalized linear mixed model which is more at risk for consistency loss at variance structure specification. [5] The trade-off of variance-structure misspecification and consistent regression coefficient estimates is loss of efficiency, yielding inflated Wald test p-values as a result of ...
"Best linear unbiased estimation and prediction under a selection model". Biometrics. 31 (2): 423– 447. doi:10.2307/2529430. JSTOR 2529430. PMID 1174616. Liu, Xu-Qing; Rong, Jian-Ying; Liu, Xiu-Ying (2008). "Best linear unbiased prediction for linear combinations in general mixed linear models". Journal of Multivariate Analysis. 99 (8): 1503 ...
When the statistical model has several parameters, however, the mean of the parameter-estimator is a vector and its variance is a matrix. The inverse matrix of the variance-matrix is called the "information matrix". Because the variance of the estimator of a parameter vector is a matrix, the problem of "minimizing the variance" is complicated.