science

Hannan–Quinn information criterion

Hannan–Quinn information criterion is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Hannan–Quinn information criterion rather than just read about it. In short: In statistics, the Hannan–Quinn information criterion (HQC) is a criterion for model selection. It is an alternative to Akaike information criterion (AIC) and Bayesian information criterion (BIC).

Key takeaways

Hannan–Quinn information criterion belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Hannan–Quinn information criterion to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Hannan–Quinn information criterion from memory before moving on to harder problems.

Reference excerpt

In statistics, the Hannan–Quinn information criterion (HQC) is a criterion for model selection. It is an alternative to Akaike information criterion (AIC) and Bayesian information criterion (BIC). It is given as

H Q C = − 2 L m a x + 2 k ln ⁡ ( ln ⁡ ( n ) ) {\displaystyle \mathrm {HQC} =-2L_{max}+2k\ln(\ln(n))\ }

Where:

L m a x {\displaystyle L_{max}} is the log-likelihood, k is the number of parameters, and n is the number of observations. According to Burnham and Anderson, HQIC, "while often cited, seems to have seen little use in practice" (p. 287). They also note that HQIC, like BIC, but unlike AIC, is not an estimator of Kullback–Leibler divergence. Claeskens and Hjort note that HQC, like BIC, but unlike AIC, is not asymptotically efficient; however, it misses the optimal estimation rate by a very small ln ⁡ ( ln ⁡ ( n ) ) {\displaystyle \ln(\ln(n))} factor (ch. 4). They further point out that whatever method is being used for fine-tuning the criterion will be more important in practice than the term ln ⁡ ( ln ⁡ ( n ) ) {\displaystyle \ln(\ln(n))} , since this latter number is small even for very large n {\displaystyle n} ; however, the ln ⁡ ( ln ⁡ ( n ) ) {\displaystyle \ln(\ln(n))} term ensures that, unlike AIC, HQC is strongly consistent. It follows from the law of the iterated logarithm that any strongly consistent method must miss efficiency by at least a ln ⁡ ( ln ⁡ ( n ) ) {\displaystyle \ln(\ln(n))} factor, so in this sense HQC is asymptotically very well-behaved. Van der Pas and Grünwald prove that model selection based on a modified Bayesian estimator, the so-called switch distribution, in many cases behaves asymptotically like HQC, while retaining the advantages of Bayesian methods such as the use of priors.

See also Akaike information criterion Bayesian information criterion Deviance information criterion Focused information criterion Shibata information criterion

References

Further reading Aznar Grasa, A. (1989). Econometric Model Selection: A New Approach, Springer. ISBN 978-0-7923-0321-3 Chen, C et al. Order Determination for Autoregressive Processes Using Resampling methods Statistica Sinica 3:1993, http://www3.stat.sinica.edu.tw/statistica/oldpdf/A3n214.pdf

Worked examples

Example 1 — a first encounter with Hannan–Quinn information criterion

Start with the simplest possible case. Write down what Hannan–Quinn information criterion claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Hannan–Quinn information criterion before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Hannan–Quinn information criterion ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Hannan–Quinn information criterion

In research: Hannan–Quinn information criterion appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Hannan–Quinn information criterion in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Hannan–Quinn information criterion is common in secondary-school and first-year university syllabi. It links to neighbouring topics Model selection, Regression variable selection, so understanding it makes those chapters shorter.
In everyday life: Look for Hannan–Quinn information criterion outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Hannan–Quinn information criterion in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Hannan–Quinn information criterion means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Hannan–Quinn information criterion out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Hannan–Quinn information criterion in simple terms?

In statistics, the Hannan–Quinn information criterion (HQC) is a criterion for model selection. It is an alternative to Akaike information criterion (AIC) and Bayesian information criterion (BIC).

Why does Hannan–Quinn information criterion matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Hannan–Quinn information criterion?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Hannan–Quinn information criterion.