Tid: 19 maj 2011 kl 11.15-12.00.

Föredragshållare: Masashi Hyodo, Tokyo University of Sciences, Japan

Titel: Some asymptotic properties of EPMC for high-dimensional linear discriminant analysis

Abstract Linear discriminat analysis (LDA) is now widely available. However, for high-dimensional data classification problem, due to the small number of samples and large number of variables, classical LDA has poor performance corresponding to the singularity and instability of the sample covariance matrix. Recently, Xu et al. (2008) suggested modified linear discriminant analysis (MLDA). On the other hand, Srivastava and  Kubokawa (2007) suggested the ridge type estimator of the covariance matrix by the empirical Bayes method. Using above ridge type estimator, Hyodo (2010) suggested ridge type linear discriminant analysis (RTLDA). Now, we are interested in the performances of MLDA and RTLDA in high-dimension. We will adopt the expected probability of misclassification (EPMC) as a standard of discrimination performance. However, it is generally difficult to obtain an explicit expression for the EPMC. So, there are much works for asymptotic properties of EPMC for LDA. The asymptotic properties under a large sample and high-dimensional framework have been studied (see, e.g., Fujikoshi and Seo (1998)). In our study, under the two-types asymptotic frameworks for high-dimensional data, we assess the asymptotic properties of EPMC for MLDA and RTLDA in high-dimension.

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