In sci.stat.consult Paige Miller <[EMAIL PROTECTED]> wrote: > Ronald Bloom wrote: >> Suppose I have more observations than I have variables. >> E.g. Say 51 variables and 30 observations apiece. >> >> The data matrix is shall we say "wide" (columns correspond >> to variables). >> >> The resulting sample covariance matrix on the covariance among >> variables is necessarily rank deficient. >> >> Is there anything useful I can learn nevertheless from >> that matrix? >> >> E.g.: >> Is there anything to be garnered from a principle components >> decomposition of this covariance matrix in this circumstance?
> Yes. Go for it. So let's say I have 51 variables. I collect them 30 days at a time. Every time I collect a new set of observations I want to assess its "surprise value", in respect of the recent past. So I have a monthly covariance matrix of rank 30. There should be 30 non-zero eigenvalues. If I get one more observation (of 51 items) can I map it into the reduced dimension subspace of size 30, and evaluate it for "extremity" using a multivariate prediction "region" using the 30x30 diagonal matrix of eigenvalues in the standard "hotelling form" on the reduced space? I'm just trying to translate theory into something I can actually practise. -Ron > -- > Paige Miller > [EMAIL PROTECTED] > http://www.kodak.com > "It's nothing until I call it!" -- Bill Klem, NL Umpire > "When you get the choice to sit it out or dance, I hope you dance" -- > Lee Ann Womack . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
