Re: Any convergence rate known about LDA?

In article <829fe43b-d7c7-42f2-bf11-f9d15eed5dab@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
<golabidoon@xxxxxxxxx> wrote:
Thank you very much Graham and Herman for your very useful answers. I
will try to find Fukunaga's book. I am very excited to learn about the
proof and how 1/sqrt(n) is derived. So Herman do you also want to
recommend a book that covers your statements? (I ask this because I am
not sure if our library has Fukunaga's book, so it will be good to
have a backup plan in case it does not have it).

Any good text on basic statistical theory will state
the asymptotic methods. A measure-theoretic probability
book is likely to have the proofs.

Thank you a lot for your answers aggain.

G.D.

On Oct 15, 11:36=A0am, hru...@xxxxxxxxxxxxxxxxxxxx (Herman Rubin) wrote:
<> In article <51230a24-cbb6-4995-b800-86d0ec12d...@xxxxxxxxxxxxxxxxxxxxxxxx=
.com>,

<> =A0<golabid...@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. =A0In that case, there is a
<> non-zero classification error rate. =A0From 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
.