Hannan–Quinn information criterion

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

$\mathrm{HQC} = -2 L_{max} + 2 k \log \log n, \$

where $L_{max}$ is the log-likelihood, k is the number of parameters, and n is the number of observations.

Burnham & Anderson (2002, p. 287) say that HQC, "while often cited, seems to have seen little use in practice". They also note that HQC, like BIC, but unlike AIC, is not an estimator of Kullback–Leibler divergence. Claeskens & Hjort (2008, ch. 4) note that HQC, like BIC, but unlike AIC, is not asymptotically efficient, and further point out that whatever method is being used for fine-tuning the criterion will be more important in practice than the term log log n, since this latter number is small even for very large n.

See also

• Deviance information criterion
• Focused information criterion

References

• Aznar Grasa, A. (1989). Econometric Model Selection: A New Approach, Springer. ISBN 978-0-7923-0321-3
• Burnham, K.P. and Anderson, D.R. (2002). Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach, 2nd ed. Springer-Verlag. ISBN 0-387-95364-7.
• Claeskens, G. and Hjort, N.L. (2008). Model Selection and Model Averaging, Cambridge.
• Hannan, E. J., and B. G. Quinn (1979), "The Determination of the order of an autoregression", Journal of the Royal Statistical Society, Series B, 41: 190–195.
• van der Pas, S.L.; Grünwald, P.D. (2014). "Almost the best of three worlds". arXiv:1408.5724.
• 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