Re: Any convergence rate known about LDA?

In article <51230a24-cbb6-4995-b800-86d0ec12dd68@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
<golabidoon@xxxxxxxxx> wrote:
Hello,

Is there any study/result on the convergence rate of Linear
Discriminant Analysis? More specifically, given two gaussian
distributions with a common covariance matrix, we would like to learn
a LDA classifier from a set of training samples. Now by convergence
rate analysis I mean if there exists any result on how fast the
expected classification error rate decreases as a function of n, where
n is the number of training samples (and perhaps how fast it grows in
p, the dimensionality of the observation space).

If the mean vectors and covariance matrix are known, the
problem becomes one-dimensional. In that case, there is a
non-zero classification error rate. From the general
theory of asymptotic distributions, the error rate should
decrease with the number n of training samples at a rate of
1/sqrt(n) to the limit rate, and this is also the case if
the covariance matrix is not known.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@xxxxxxxxxxxxxxx Phone: (765)494-6054 FAX: (765)494-0558
.

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