Kullback Information Criterion for a Simultaneous Equations Model

Warangkhana  Riansut

Authors

Warangkhana Riansut Mathematics and Data Management Program, Faculty of Science and Digital Innovation, Thaksin University, Phatthalung, Thailand

Keywords:

Model selection criterion, selection of model order, L2 efficiency, maximum likelihood estimator (MLE)

Abstract

This paper introduces a new model selection criterion, SKIC(MLE), for simultaneous equations modelling based on the Kullback information criterion (KIC) using a maximum likelihood estimator (MLE). A comprehensive comparative simulation study demonstrates that when dealing with small sample sizes, SKIC(MLE) outperforms SKIC, a criterion proposed by Keerativibool and Jitthavech
(2015). The results indicate that the proposed criterion, SKIC(MLE), has the potential to improve the accuracy of model selection significantly and exhibits higher observed L2 efficiency than SKIC in such scenarios. The superiority of SKIC(MLE) in small sample sizes is attributed to the fact that the penalty term of SKIC increases exponentially as the number of parameters increases, causing the SKIC
value to be higher than SKIC(MLE). As a result, SKIC is more likely to select underfitting models or few parameters than SKIC(MLE). However, this issue is not prevalent in medium to large sample sizes, so SKIC outperforms SKIC(MLE). This research has significant practical implications, potentially revolutionizing simultaneous equations modelling in cases with small sample sizes.

References

Akaike H. A new look at the statistical model identification. IEEE Trans Automat Contr. 1974; 19(6): 716-723.

Anderson TW. An introduction to multivariate statistical analysis. 3rd ed. New Jersey: John Wiley & Sons; 2003.

Cavanaugh JE. A large-sample model selection criterion based on Kullback’s symmetric divergence. Stat Prob Lett. 1999; 42(4): 333-343.

Cavanaugh JE. Criteria for linear model selection based on Kullback’s symmetric divergence. Aust N Z J Stat. 2004; 46(2): 257-274.

Greene W. Econometric analysis. 6th ed. New Jersey: Prentice-Hall; 2008.

Hurvich CM, Tsai CL. Regression and time series model selection in small samples. Biometrika. 1989; 76(2): 297-307.

Johnson RA, Wichern DW. Applied multivariate statistical analysis. 4th ed. New Jersey: Prentice Hall; 1998.

Keerativibool W, Jitthavech J, Lorchirachoonkul V. Model selection in a system of simultaneous equations model. Commun Stat Theory Methods. 2011; 40(3): 373-393.

Keerativibool W. Study on the penalty functions of model selection criteria. Thail Stat. 2014; 12(2): 161-178.

Keerativibool W, Jitthavech J. Model selection criterion based on Kullback-Leibler’s symmetric divergence for simultaneous equations model. Chiang Mai J Sci. 2015; 42(3): 761-773.

McQuarrie AD, Tsai CL. Regression and time series model selection. Singapore: World Scientific Pub Co Inc; 1998.

McQuarrie ADR, Shumway RH, Tsai CL. The model selection criterion AICu. Stat. Prob Lett. 1997; 34(3): 285-292.

Niyonzima F. A new method for regression model selection. Global Sci J. 2020; 8(2): 1858-1899.

Perez-Sanchez B, Gonzalez M, Perea C, Lopez-Espin JJ. A new computational method for estimating simultaneous equations models using entropy as a parameter criteria. Mathematics. 2021; 9(700): 1-9.

Pham H. A new criterion for model selection. Mathematics. 2019; 7(12): 1215, https://doi.org/10.3390/math7121215

Rossi R, Murari A, Gaudio P, Gelfusa M. Upgrading model selection criteria with goodness of fit tests for practical applications. Entropy. 2020; 22(447): 1-13.

Schwarz G. Estimating the dimension of a model. Ann Stat. 1978; 6(2): 461-464.

Zhang J, Yang Y, Ding J. Information criteria for model selection. WIREs Comp Stats. 2023; 15(5): 1-27.