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Thomas Gueuning, KULeuven Print
Thursday, 06 October 2016, 12:15 - 13:15

Thomas Gueuning, KULeuven

A High-dimensional Focused Information Criterion

Abstract: Most variable selection procedures have in common that they select one single best model that is used to estimate all the quantities of interest related to the data. This is the case for popular information criteria such as the AIC and the BIC and for penalization procedures such as the LASSO and the SCAD. The Focused Information Criterion (FIC) departs from these methods by performing focused driven variable selection. The FIC selects the model that best estimates a particular quantity of interest (the focus) in terms of mean squared error (MSE). Consequently, different models can be selected for different quantities of interest and the FIC can provide estimators with smaller MSE. An example of such a quantity of interest is the prediction for a new particular observation of the covariates.  The current FIC literature is restricted to the low-dimensional case. In this paper, we show that the FIC idea can be extended to high-dimensional data.  We distinguish two cases: (i) the considered submodel is of low-dimension and (ii) the considered submodel is of high-dimension. In the former case, we obtain an alternative low-dimensional FIC formula that can directly be applied. In the latter case we use a desparsified estimator that allows us to derive the MSE of the focus estimator. We illustrate the performance of the high-dimensional FIC with a numerical study and a real dataset example.

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