where 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; however, it misses the optimal estimation rate by a very small factor. They further point out that whatever method is being used for fine-tuning the criterion will be more important in practice than the term , since this latter number is small even for very large ; however, the 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 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 etc.
Aznar Grasa, A. (1989). Econometric Model Selection: A New Approach, Springer. ISBN978-0-7923-0321-3
Burnham, K.P. and Anderson, D.R. (2002). Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach, 2nd ed. Springer-Verlag. ISBN0-387-95364-7.
hannan, quinn, information, criterion, statistics, criterion, model, selection, alternative, akaike, information, criterion, bayesian, information, criterion, given, displaystyle, mathrm, where, displaystyle, likelihood, number, parameters, number, observation. 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 Burnham amp 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 amp Hjort 2008 ch 4 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 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 Grunwald 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 etc See also editAkaike information criterion Bayesian information criterion Deviance information criterion Focused information criterion Shibata information criterionReferences editAznar 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 Grunwald P D 2017 Almost the best of three worlds To appear in Statistica Sinica DOI 10 5705 ss 202016 0011 2017 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 Retrieved from https en wikipedia org w index php title Hannan Quinn information criterion amp oldid 1159794379, wikipedia, wiki, book, books, library,
