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A model selection criterion for discriminant analysis of high-dimensional data with fewer observations |
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| Authors: | Masashi Hyodo Takayuki Yamada Muni S Srivastava |
| Institution: | 1. JSPS Research Fellow, Graduate School of Economics, The University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo 113-0033, Japan;2. Risk Analysis Research Center, The Institute of Statistical Mathematics, 10-3 Midori-cho, Tachikawa, Tokyo 190-8562, Japan;3. Department of Statistics, University of Toronto, 100 St. George Street, Toronto, Ontario, Canada M5S 3G3 |
| Abstract: | This paper is concerned with the problem of selecting variables in two-group discriminant analysis for high-dimensional data with fewer observations than the dimension. We consider a selection criterion based on approximately unbiased for AIC type of risk. When the dimension is large compared to the sample size, AIC type of risk cannot be defined. We propose AIC by replacing maximum likelihood estimator with ridge-type estimator. This idea follows Srivastava and Kubokawa (2008). It has been further extended by Yamamura et al. (2010). Simulation revealed that the proposed AIC performs well. |
| Keywords: | Akaike information criterion Discriminant analysis Ridge-type estimator High dimensional data |
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