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The model selection criterion AICu

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  • McQuarrie, Allan
  • Shumway, Robert
  • Tsai, Chih-Ling

Abstract

For regression and time series model selection, Hurvich and Tsai (1989) obtained a bias correction Akaike information criterion, AICc, which provides better model order choices than the Akaike information criterion, AIC (Akaike, 1973). In this paper, we propose an alternative improved regression model selection criterion, AICu, which is an approximate unbiased estimator of Kullback-Leibler information. We show that AICu is neither a consistent (Shibata, 1986) nor an efficient (Shibata, 1980, 1981) criterion. Our simulation studies indicate that the behavior of AICu is a compromise between that of efficient (AICc) and consistent (BIC, Akaike, 1978) criteria. Specifically, AICu performs better than AICc for moderate to large sample sizes except when the true model is of infinite order. In addition, it outperforms BIC except when a true model exists and the sample size is large.

Suggested Citation

  • McQuarrie, Allan & Shumway, Robert & Tsai, Chih-Ling, 1997. "The model selection criterion AICu," Statistics & Probability Letters, Elsevier, vol. 34(3), pages 285-292, June.
    • Handle: RePEc:eee:stapro:v:34:y:1997:i:3:p:285-292
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    Cited by:

    1. Jan G. de Gooijer & Antoni Vidiella-i-Anguera, 2000. "Modelling Seasonalities in Nonlinear Inflation Rates using SEASETARs," Tinbergen Institute Discussion Papers 00-098/4, Tinbergen Institute.
    2. De Gooijer, Jan G. & Vidiella-i-Anguera, Antoni, 2003. "Nonlinear stochastic inflation modelling using SEASETARs," Insurance: Mathematics and Economics, Elsevier, vol. 32(1), pages 3-18, February.
    3. Rinke Saskia & Sibbertsen Philipp, 2016. "Information criteria for nonlinear time series models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 20(3), pages 325-341, June.
    4. Fábio Bayer & Francisco Cribari-Neto, 2015. "Bootstrap-based model selection criteria for beta regressions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(4), pages 776-795, December.
    5. Alessio Anzuini & Luca Rossi, 2022. "Unconventional monetary policies and expectations on economic variables," Empirical Economics, Springer, vol. 63(6), pages 3027-3043, December.
    6. Galeano, Pedro, 2004. "Model selection criteria and quadratic discrimination in ARMA and SETAR time series models," DES - Working Papers. Statistics and Econometrics. WS ws041406, Universidad Carlos III de Madrid. Departamento de Estadística.
    7. Sýdýka Baþçý & Asad Zaman & Arzdar Kiracý, 2010. "Variance Estimates and Model Selection," International Econometric Review (IER), Econometric Research Association, vol. 2(2), pages 57-72, September.
    8. Bentolhoda Asl-Rousta & S. Jamshid Mousavi & Majid Ehtiat & Mehdi Ahmadi, 2018. "SWAT-Based Hydrological Modelling Using Model Selection Criteria," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 32(6), pages 2181-2197, April.
    9. Salvatore Ingrassia & Antonio Punzo & Giorgio Vittadini & Simona Minotti, 2015. "The Generalized Linear Mixed Cluster-Weighted Model," Journal of Classification, Springer;The Classification Society, vol. 32(1), pages 85-113, April.
    10. McQuarrie, Allan & Tsai, Chih-Ling, 1999. "Model selection in orthogonal regression," Statistics & Probability Letters, Elsevier, vol. 45(4), pages 341-349, December.
    11. Rinke, Saskia, 2016. "The Influence of Additive Outliers on the Performance of Information Criteria to Detect Nonlinearity," Hannover Economic Papers (HEP) dp-575, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    12. Fernández, D. & Arnold, R. & Pledger, S., 2016. "Mixture-based clustering for the ordered stereotype model," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 46-75.
    13. Eleni Matechou & Ivy Liu & Daniel Fernández & Miguel Farias & Bergljot Gjelsvik, 2016. "Biclustering Models for Two-Mode Ordinal Data," Psychometrika, Springer;The Psychometric Society, vol. 81(3), pages 611-624, September.
    14. Hacker, Scott, 2010. "The Effectiveness of Information Criteria in Determining Unit Root and Trend Status," Working Paper Series in Economics and Institutions of Innovation 213, Royal Institute of Technology, CESIS - Centre of Excellence for Science and Innovation Studies.
    15. Salvatore Ingrassia & Antonio Punzo & Giorgio Vittadini & Simona Minotti, 2015. "Erratum to: The Generalized Linear Mixed Cluster-Weighted Model," Journal of Classification, Springer;The Classification Society, vol. 32(2), pages 327-355, July.
    16. R. Scott Hacker & Abdulnasser Hatemi-J, 2021. "Model selection in time series analysis: using information criteria as an alternative to hypothesis testing," Journal of Economic Studies, Emerald Group Publishing Limited, vol. 49(6), pages 1055-1075, September.
    17. Lee, Shyan-Yuan & Tsai, Chih-Ling, 1998. "Model selection for causal models: The global procedure with AICC and AICU," Global Finance Journal, Elsevier, vol. 9(2), pages 205-223.
    18. Antonello Maruotti, 2015. "Handling non-ignorable dropouts in longitudinal data: a conditional model based on a latent Markov heterogeneity structure," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(1), pages 84-109, March.

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