*Tid:* **19 maj 2011 kl 11.15-12.00.**
**Seminarierummet 3721**, Institutionen för
matematik, KTH, Lindstedts väg 25.
Karta!
*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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