Focused Information Criterion

Select a candidate statistical model by the estimated risk of its estimator for a declared focus parameter, allowing the preferred model to change when the inferential target changes.

Version

v3 · 2026-09-06 · History

Domain-specific #

1861

Origin domain

statistics

Subdomain

statistical model selection

Aliases

Focussed Information Criterion, FIC

Core Idea

The Focused Information Criterion (FIC) is a statistical model-selection method that asks which candidate model estimates a declared focus parameter most accurately. The focus, written mu, is an estimand meaningful under every candidate model: a regression mean at a specified covariate value, a quantile, a treatment contrast, a survival probability at a chosen time and patient profile, or another scientifically chosen functional. Candidate model S supplies an estimator mu_hat_S. FIC estimates the risk of that estimator for this particular focus and selects a candidate with minimum estimated focus risk. Change the focus and the selected model may legitimately change.

Scope of Application

FIC applies where several plausible statistical models estimate the same scientifically meaningful quantity and the analyst can derive or approximate each estimator's risk under a defensible comparison regime. Its original scope is large-sample likelihood inference over nested submodels. Subsequent formulations cover regression, generalized linear models, survival analysis, semiparametric and nonparametric settings, quantile targets, time series, high-dimensional procedures, and focused model averaging. The domain can change; the common-focus and risk-estimation obligations do not.

Clarity

FIC forces the phrase “best model” to be completed. The analyst must name the target, the loss, the candidate class, and the regime under which the score estimates risk. This turns an ambiguous global superlative into an auditable conditional claim: “among these candidates, under this local-misspecification approximation and squared-error loss, model S has the smallest estimated risk for mu.”

Manages Complexity

Model-selection complexity grows combinatorially when q optional parameters produce up to 2^q submodels. FIC gives these candidates a common focus-specific currency. Once the wide-model information, focus derivatives, and subset projections are computed, many candidate risks can be compared without separately inventing a scientific objective for every model.

Abstract Reasoning

Focus invariance check. Verify that mu(theta,gamma) denotes one quantity under every candidate. Parameter names alone do not establish this; transformations, links, and conditional-versus-marginal interpretations can change the estimand.

Local experiment. In the original theory, place the true parameter at gamma_0 + delta/sqrt(n). For each subset S, derive the limiting distribution of sqrt(n)(mu_hat_S-mu_true). The focus gradient converts omitted parameter directions into bias; the information matrix converts estimated directions into variance.

Knowledge Transfer

Within statistics, FIC transfers by preserving roles rather than formulas. A generalized linear model changes the likelihood and focus derivative; a Cox model adds a baseline hazard and censoring structure; a semiparametric model changes nuisance estimation; a quantile target changes the estimator and risk. In every case, the analyst can ask: What is the common focus? What candidate estimators exist? What is their focus risk? Which terms estimate bias and variance? Which model minimizes the justified estimate?

Relationships to Other Abstractions

Current abstraction Focused Information Criterion Domain-specific

Parents (2) — more general patterns this builds on

• Focused Information Criterion is a kind of Selection Prime

  prime:selection — proposed strict subsumption parent. FIC takes a candidate population and a focus-risk criterion, then gives one or more models greater retention.

• Focused Information Criterion presupposes Statistical Inference Prime

  prime:statistical_inference — proposed strict presupposition parent. Focus estimators, limiting distributions, information matrices, and model-selection risk are meaningful only inside sample-to-process reasoning with quantified.

Hierarchy paths (5) — routes to 5 parentless roots

• Focused Information Criterion → Selection

Show alternative paths (4)

Neighborhood in Abstraction Space

Focused Information Criterion sits in a sparse region of the domain-specific corpus (75^th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Unclustered & Miscellaneous (1565 abstractions)

Nearest neighbors

• Variational Bayesian Methods — 0.84
• Learnable Function Class — 0.83
• Regression — 0.83
• Optimality criterion — 0.83
• Statistical Contrast — 0.83

Computed from structural-signature embeddings · 2026-09-08