Abstract
The main motivation for Hannan and Quinn’s ϕ criterion is the minimality of its log log n penalty rate, which is the slowest one compatible with consistency. Unlike Akaike’s AIC, based on the minimization of some estimated mean Kullback-Leibler distance, or Rissanen and Schwarz’s BIC,which minimizes an estimate of the expected complexity, Hannan and Quinn’s ϕ at first sight is not connected with any sound decision-theoretic or statistical principle. The objective of this paper is to provide a stochastic complexity justification and an information-theoretic derivation for ϕ Two generalized AIC — BIC — ϕ criteria also are proposed. Both are derived from Kullback-Leibler distance arguments, and enjoy the same consistency properties as BIC (strong consistency) and ϕ (weak consistency), respectively.
Research supported by the Fonds d’Encouragement à la Recherche de l’Université Libre de Bruxelles and the Human Capital and Mobility contract ERB CT CHRX 940 963.
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© 1996 Springer-Verlag New York, Inc.
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El Matouat, A., Hallin, M. (1996). Order Selection, Stochastic Complexity and Kullback-Leibler Information. In: Robinson, P.M., Rosenblatt, M. (eds) Athens Conference on Applied Probability and Time Series Analysis. Lecture Notes in Statistics, vol 115. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2412-9_21
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DOI: https://doi.org/10.1007/978-1-4612-2412-9_21
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