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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.
Heckman also developed a two-step control function approach to estimate this model, [3] which avoids the computational burden of having to estimate both equations jointly, albeit at the cost of inefficiency. [4] Heckman received the Nobel Memorial Prize in Economic Sciences in 2000 for his work in this field. [5]
A basic tool for econometrics is the multiple linear regression model. [8] Econometric theory uses statistical theory and mathematical statistics to evaluate and develop econometric methods. [ 9 ] [ 10 ] Econometricians try to find estimators that have desirable statistical properties including unbiasedness , efficiency , and consistency .
A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of sample data (and similar data from a larger population). A statistical model represents, often in considerably idealized form, the data-generating process . [ 1 ]
"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 ...
The general ARMA model was described in the 1951 thesis of Peter Whittle, who used mathematical analysis (Laurent series and Fourier analysis) and statistical inference. [ 12 ] [ 13 ] ARMA models were popularized by a 1970 book by George E. P. Box and Jenkins, who expounded an iterative ( Box–Jenkins ) method for choosing and estimating them.
In statistics and econometrics, the first-difference (FD) estimator is an estimator used to address the problem of omitted variables with panel data. It is consistent under the assumptions of the fixed effects model .
It is a model-free measure in the sense that it simply relies on calculating the estimator again with a different sample. On the right is Tukey's biweight function, which, as we will later see, is an example of what a "good" (in a sense defined later on) empirical influence function should look like.