Focused Information Criteria

Abstract

The focused information criterion is used to make a choice among several statistical models, or among several variables to include in a model. Different from other such information criteria, the focused information criterion is constructed to select the best model for a given interest quantity, the focus of the research question. Different such focus parameters may lead to different selected models, each one best for the corresponding focus. What is `best' is defined by a risk function, often the mean squared error. Other risks can be considered too for focused selection. Selections by the focused information criterion include using parametric (generalized) linear models, non- and semiparametric models, quantile regression models, graphical models, models for survival data, for longitudinal data, time series models, and many more. Extensions of the basic version include versions for high-dimensional data, regularized estimation, and Bayesian methods.

29 pages, 5 figures. Invited FIC review paper for the Annual Review of Statistics and Its Application; will appear there in similar form, modulo layouting, and with an online Supplementary Material section