In article <[EMAIL PROTECTED]>, Elliot Cramer <[EMAIL PROTECTED]> wrote: >In sci.stat.edu Eric Zivot <[EMAIL PROTECTED]> wrote: >: In the finance literature, it is common to do pca in a situation in which >: there are more variables than observation (e.g returns on 1000 assets and >: 500 observations). >This says alot about the finance literature
>In this case, one uses what has been called "asymptotic >: principal component analysis". In stead of eigenvalue analysis on the >: non-invertible N x N covariance RR' (R is N x T, N >> T), do eigen value >: analysis on the smaller T x T matrix R'R. >There is nothing asymptotic about it; it is simple mathematics >(A'A)x = kx (x an eigen vector, k the value) >(AA')(Ax) = k(Ax) >the eigenvalues are the same and you solve for the original vectors. >so what? it's still dumb to do anything with more variables than >observations I agree that there is nothing asymptotic, unless one wishes to look at what happens as the number of variables gets large. I agree that PC is not good here, but I would say this about all uses of PC. In fact, one should rarely use correlations; their distribution properties do not behave. If one does not use correlations, scaling messes it up. This does not apply to the use of principal components on two sets of variables. As for it being dumb to do anything with more variables than observations, it MUST be done. Arbitrarily discarding variables is not what should be done. However, one cannot just use the "cookbook"; it is necessary to think. But should one ever just use the cookbook? -- 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, Deptartment of Statistics, Purdue University [EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558 . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
