On Relationship Between the AIC and the Overall Error Rates for Selection of Variables in a Discriminant Analysis
This paper deals with the problem of selecting the “best” subset of variables in a discriminant analysis with the aim of allocating future observations, in the context of two multivariate normal populations with the same covariance matrix. We consider the methods based on the following three criteria: (i) the AIC for the “no additional information” model, (ii) the overall error rate criterion based on the linear classification statistic and (iii) the overall error rate criterion based on the ML classification statistic. It is shown that there is a close relationship between the AIC and the overall error rate criteria.
KeywordsError Rate Discriminant Analysis Asymptotic Expansion Asymptotic Distribution Classification Statistic
Unable to display preview. Download preview PDF.
- Akaike, H. (1973). ‘Information theory and an extension of the maximum likelihood principle’. In: 2nd International Symposium on Information Theory (B. N. Petrov and F. Czáki, eds.), pp.267–281, Akademiai Kiadó, Budapest.Google Scholar
- Fujikoshi, Y. (1985 b). ‘Selection of variables in discriminant analysis and canonical correlation analysis. In: Multivariate Analysis — VI (P. R. Krishnaiah, ed.), pp.219–236, North-Holland.Google Scholar
- Rao, C. R. (1970). ‘Inference on discriminant function coefficients’. In: Essays in Prob, and Statist. (R. C. Bose, ed.), pp.587–602. Univ. of North Carolina Press, Chapel Hill.Google Scholar