International Statistical Review

Estimation Optimality of Corrected AIC and Modified Cp in Linear Regression

Simon L. Davies, Andrew A. Neath, and Joseph E. Cavanaugh

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Abstract

Model selection criteria often arise by constructing unbiased or approximately unbiased estimators of measures known as expected overall discrepancies (Linhart & Zucchini, 1986, p. 19). Such measures quantify the disparity between the true model (i.e., the model which generated the observed data) and a fitted candidate model. For linear regression with normally distributed error terms, the "corrected" Akaike information criterion and the "modified" conceptual predictive statistic have been proposed as exactly unbiased estimators of their respective target discrepancies. We expand on previous work to additionally show that these criteria achieve minimum variance within the class of unbiased estimators.

Article information

Source
Internat. Statist. Rev., Volume 74, Number 2 (2006), 161-168.

Dates
First available in Project Euclid: 24 July 2006

Permanent link to this document
https://projecteuclid.org/euclid.isr/1153748790

Keywords
AICc Gauss discrepancy Kullback-Leibler discrepancy MC_p Model selection criteria

Citation

Davies, Simon L.; Neath, Andrew A.; Cavanaugh, Joseph E. Estimation Optimality of Corrected AIC and Modified Cp in Linear Regression. Internat. Statist. Rev. 74 (2006), no. 2, 161--168. https://projecteuclid.org/euclid.isr/1153748790


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References

  • [1] Akaike, H. (1973). Information Theory and an Extension of the Maximum Likelihood Principle. In 2nd International Symposium on Information Theory, Eds. B. N. Petrov and F. Csáki, pp. {267-281}. Budapest: Akadémia Kiadó.
  • [2] Akaike, H. (1974). A New Look at the Statistical Model Identification. IEEE Transactions on Automatic Control, AC-19, {716-723}.
  • [3] Christensen, R. (1996). Plane Answers to Complex Questions (2nd Edition). New York: Springer.
  • [4] Fujikoshi, Y. & Satoh, K. (1997). Modified AIC and \mbox{C}_{p} in Multivariate Linear Regression. Biometrika, 84, {707-716}.
  • [5] Hurvich, C.M. & Tsai, C.L. (1989). Regression and Time Series Model Selection in Small Samples. Biometrika, 76, {297-307}.
  • [6] Kotz, S., Johnson, N.L. & Read, C.B., Eds. (1982). Encyclopedia of Statistical Sciences, Volume 2. New York: Wiley.
  • [7] Kullback, S. (1968). Information Theory and Statistics. New York: Dover.
  • [8] Linhart, H. & Zucchini, W. (1986). Model Selection. New York: Wiley.
  • [9] Mallows, C.L. (1973). Some Comments on \mbox{C}_{\mbox{p}}. Technometrics, 15, {661-675}.
  • [10] Sugiura, N. (1978). Further Analysis of the Data by Akaike's Information Criterion and the Finite Corrections. Communications in Statistics, A7, {13-26}.