Share This Article:

On Asymptotic Properties of AIC Variants with Applications

Abstract Full-Text HTML Download Download as PDF (Size:108KB) PP. 105-109
DOI: 10.4236/ojs.2011.12012    4,558 Downloads   7,781 Views   Citations

ABSTRACT

In statistical modeling, the investigator is frequently confronted with the problem of selecting an appropriate model from a general class of candidate models. In recent years, various model selection procedures that can be used for the selection of the best possible model have been proposed. The AIC criterion [1] is considered the most popular tool for model selection although many competitors have been introduced over the years. One of the main drawbacks of AIC is its tendency to favor high dimensional models namely to overestimate the true model. A second issue that needs the attention of the investigator is the presence of outlying observations in the data set the inclusion of which in the statistical analysis may lead to erroneous results. In this work we propose AIC variants to handle the above weaknesses. Furthermore the asymptotic properties of the proposed criteria are investigated and a number of applications are discussed.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

A. Karagrigoriou, K. Mattheou and I. Vonta, "On Asymptotic Properties of AIC Variants with Applications," Open Journal of Statistics, Vol. 1 No. 2, 2011, pp. 105-109. doi: 10.4236/ojs.2011.12012.

References

[1] H. Akaike, “Information Theory and an Extension of the Maximum Likelihood Principle,” Proceeding of 2nd International Symposium on Information Theory, Vol. 1, No. 1973, 1973, pp. 267-281.
[2] B. Efron, “Estimating the Error Rate of a Prediction Rule: Improvement on Cross Validationn,” Journal of the American Statistical Association, Vol. 78, No. 382, 1983, pp. 316-331. doi:10.2307/2288636
[3] B. Efron and R. J. Tibshirani, “An Introduction to Bootstrap,” Chapman and Hall, New York, 1993.
[4] J. E. Cavanaugh, and R. H. Shumway, “A Bootstrap Variant of AIC for State-Space Model Selection,” Statistica Sinica, Vol. 7, No. 2, 1997, pp. 473-496.
[5] G. Schwarz, “Estimating the Dimension of a Model,” The Annals of Statistics, Vol. 6, No. 2, 1978, pp. 461-464. doi:10.1214/aos/1176344136
[6] C. M. Hurvich and C. L. Tsai, “Regression and Time Series Model Selection in Small Samples,” Biometrika, Vol. 76, No. 2, 1989, pp. 297-307. doi:10.1093/biomet/76.2.297
[7] R. Shibata, “Selection of the Order of an Autoregressive Model by Akaike’s Information Criterion,” Biometrika, Vol. 63, No. 1, 1976, pp. 117-126. doi:10.1093/biomet/63.1.117
[8] A. Karagrigoriou, “Asymptotic Efficiency of Model Selection Criteria: The Nonzero Mean Gaussian AR(Infinity) Case,” Communications in Statistics: Theory and Methods, Vol. 24, No. 4, 1995, pp. 911-930. doi:10.1080/03610929508831530
[9] C. Z. Wei, “On Predictive Least Squares Principles,” The Annals of Statistics, Vol. 20, No. 1, 1992, pp. 1-42. doi:10.1214/aos/1176348511
[10] R. Shibata, “Asymptotically Efficient Selection of the Order of the Model for Estimating Parameters of Linear Process,” The Annals of Statistics, Vol. 8, No. 1, 1980, pp. 147-164. doi:10.1214/aos/1176344897
[11] A. Karagrigoriou, “Asymptotic Efficiency of the Order Selection of a Nongaussian AR Process,” Statistica Sinica, Vol. 7, 1997, pp. 407-423.
[12] S. Lee and A. Karagrigoriou, “An Asymptotically Optimal Selection of the Order of a Linear Process,” Sankhyā: The Indian Journal of Statistics, Series A, Vol. 63, No. 1, 2001, pp. 93-106.
[13] H. Woods, H. H. Steinour and H. R. Starke, “Effect of Composition of Portland Cement on Heat Evolved during Hardening,” Industrial and Engineer Chemistry, Vol. 24, No. 11, 1932, 1207-1214. doi:10.1021/ie50275a002
[14] N. Draper and H. Smith, “Applied Regression Analysis,” 2nd Edition, John Wiley, New York, 1981.

  
comments powered by Disqus

Copyright © 2019 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.