Hannan–Quinn information criterion¶
In statistics, the Hannan–Quinn information criterion (HQC) is a criterion for model selection.
Core Idea¶
The Hannan–Quinn information criterion is a likelihood-based rule for selecting among fitted statistical models while penalizing unnecessary parameters. In a common form, HQC = -2 log Lmax + 2k log log n, where Lmax is the maximized likelihood, k the number of estimated parameters, and n the sample size; the candidate with the smallest value is preferred. Fit lowers the first term, while complexity raises the second, so a parameter is retained only when its improvement in likelihood outweighs the slowly increasing penalty. The log log n penalty places Hannan–Quinn between familiar alternatives asymptotically.
Scope of Application¶
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Autoregressive order selection. Candidate lag orders fitted to the same series receive comparable likelihood and parameter counts.
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Time-series model comparison. The criterion balances improved fit against additional dynamic parameters.
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Asymptotic theory. The log-log penalty is studied near the rate needed for strong consistency in relevant settings.
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AIC comparison. HQC's diverging penalty is contrasted with predictive-efficiency objectives and persistent overfit risk.
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BIC comparison. Its weaker-than-log-n penalty reveals a different fit–parsimony tradeoff.
Clarity¶
Hannan–Quinn information criterion balances maximized likelihood against a parameter penalty growing as \(2k\log\log n\) under a common convention. It is not a universal measure of model truth, and constants, effective sample size, likelihood comparability, and candidate family must be stated. Its asymptotic rationale differs from AIC's predictive target and BIC's stronger penalty.
Manages Complexity¶
Hannan–Quinn criterion compresses each fitted candidate model to maximized likelihood, parameter count, sample size, and one penalty formula. The analyst ranks models by a single comparable score while retaining the fit–complexity tradeoff. AIC, HQC, and BIC branches differ chiefly in penalty growth and asymptotic objective, so selection behavior can be anticipated without re-deriving each method.
Abstract Reasoning¶
Penalization move. Combine maximized log-likelihood with the Hannan–Quinn parameter penalty involving log log sample size to score candidate models. Selection move. Choose the lowest criterion among models fitted to the same observations under compatible likelihood conventions. Asymptotic move. Use the penalty's growth to reason about strong consistency under the theorem's regularity and candidate-model assumptions. Diagnostic move. Compare HQC with AIC, BIC, residual evidence, and stability rather than treating a small score difference as decisive. Boundary move.
Knowledge Transfer¶
Within the home domain. The Hannan–Quinn information criterion transfers across time-series, regression, econometrics, and statistical model selection when maximized likelihood is balanced against its specific log-log sample-size penalty. Sample size, parameter count, likelihood convention, candidate set, and asymptotic consistency retain roles. Beyond the home domain (C — selection criterion). It applies literally to compatible fitted models in any discipline. Its boundary is inferential: scores compare only the supplied candidates, small differences may be unstable, regularity assumptions matter, and HQC is not a p-value, causal test, cross-validation estimate, or guarantee of best finite-sample prediction.
Relationships to Other Abstractions¶
Current abstraction Hannan–Quinn information criterion Domain-specific
Parents (1) — more general patterns this builds on
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Hannan–Quinn information criterion is a kind of Evaluation Prime
Hannan–Quinn information criterion is a domain-specific kind of Evaluation: In statistics, the Hannan–Quinn information criterion (HQC) is a criterion for model selection.
Hierarchy path (1) — routes to 1 parentless root
- Hannan–Quinn information criterion → Evaluation → Comparison → Self Checking
Neighborhood in Abstraction Space¶
Hannan–Quinn information criterion sits in a sparse region of the domain-specific corpus (68th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.
Family — Unclustered & Miscellaneous (2551 abstractions)
Nearest neighbors
- Optimality criterion — 0.85
- Bayes Factor — 0.85
- Machine-Learning Learning Curve — 0.85
- Focused Information Criterion — 0.84
- Expectation–Maximization Algorithm — 0.83
Computed from structural-signature embeddings · 2026-10-08