It has been suggested to me that if I construct a covariance or correlation matrix using factor model then I can use the Marchenko-Pastur distribution to highlight significant correlations (or covariance levels). Can someone explain how this is done? On a more general note can someone also suggest a good reference for an introduction to the Marchenko-Pastur distribution and it's applications?
You get eigenvalues of the correlation matrix. Marchenko-Pastur will tell you the threshold under which you can drop the eigenvalues. For instance, take a look at this dissertation p.24 where they use the theorem.
What eigen decomposition does here is it lets you identivy a few important factors that represent entire correlation matrix. Instead of dealing with a full correlation matrix NxN where N is the number of variables/dimensions, you reduce it to MxN where M is number of top eigen vectors.