Focused Information Criteria

2026-08-02

AI Summary

This work proposes the Focused Information Criterion (FIC), a model selection framework that departs from the conventional pursuit of global optimality by tailoring model choice to a user-specified target parameter or risk function—such as mean squared error—thereby prioritizing relevance to the inferential goal at hand. Unlike traditional criteria, FIC dynamically selects the model that minimizes the estimated risk for the quantity of interest, accommodating diverse modeling paradigms including linear, nonparametric, quantile regression, and graphical models. The approach further extends to high-dimensional, longitudinal, survival, and time series data through integration with regularization techniques, Bayesian estimation, and targeted risk optimization. This yields a unified and flexible framework for “goal-oriented” optimal modeling, where the best model is defined not universally but relative to the specific objective of the analysis.

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.

Problem

• focused information criterion
• model selection
• focus parameter
• risk function
• statistical models

Innovation

• Focused Information Criterion
• Model Selection
• Focus Parameter
• Risk Function
• High-dimensional Data