|
From: | Vic Norton |
Subject: | Re: QR vs LU factorisation |
Date: | Tue, 1 Jul 2008 11:18:28 -0400 |
Here is the kind of "noisy" data problem I am thinking of. Suppose you are interested in 50 equity "funds" and you have 50 vectors of 39 successive 13-week returns. Then you can compute 50 expected returns (assuming some kind of weighting, perhaps uniform, of the individual returns) and 50 vectors of deviations from these expected returns. Think of the deviation vectors as the risks of the individual funds. Your problem: express expected return as a linear function of risk.
For this problem you want to solve e' * R = Efor the 39 x 1 expected return vector e, where R is the 39 x 50 risk matrix and E is the 1 x 50 matrix of expected returns. None of your data, being ultimately based on dollars and cents prices per share, has even 6 digit accuracy. This is a problem where the svd approach with svdcut = 1e-6 would seem to be a natural choice. But you definitely would NOT compute the "pseudoinverse" of R to solve the problem.
Regards, Vic On Jul 1, 2008, at 4:41 AM, Fredrik Lingvall wrote:
Vic Norton wrote:What type of problem is this about? If it is parameter estimation from noisy data then you can't really speak about an "inverse" but you can formulate the problem as an inference problem (e.g., find the most likely estimate given your data and background info (noise variance etc.).On Jun 30, 2008, at 5:16 PM, Jaroslav Hajek wrote:SVD is the best solution in this case. For example, to invert a matrix A choose an svd "precision", say svdcut = 1e-12; Then do [U S V] = svd(A, 1); sig = diag(S); rnk = 0; for i = 1 : length(sig) if sig(i)/sig(1) < svdcut; break; endif rnk++; endfor Ainv = ( V(:, 1:rnk) * diag(1 ./ sig(1:rnk)) ) * U(:, 1:rnk)'; to get the (pseudo)inverse of A.or just use "pinv".What is the "precision" of "pinv"? If your data only is accurate to 6 digits, why try for anything more accurate than svdcut = 1e-7 would produce? Any additional "accuracy" is pure noise./Fredrik
[Prev in Thread] | Current Thread | [Next in Thread] |