I am newby in statistics and I have huge data with "p" variables and "n" samples. My data is a two dimensional matrix with "n" columns (each column is a sample) and "p" rows (each row is a variable). I would like to find the partial correlation between "p" variables and write them in a p×p matrix. For example I want to fine the partial correlations between variable 1 and 2, variable 1 and 3 and .... fianlly variable p and p. At first I must make a variance-covariance matrix Σ and then inverse it to make a new matrix called omega which is a partial covariance matrix. By using omega I can simply find partial correlations by a simple formula. But before getting partial correlations, I must optimize omega matrix to make it sparser.
I have chosen Concord regression algorithm for omega optimization. This algorithm is a multivariate regression and for starting this regression my data must have some special charachteristics. In the article it is written that: "Let the random vector Yk = (y1 k, y2 k, ... , yp k )', k = 1, 2, ... , n, denote independent and identically distributed (IID) observations from a multivariate distribution with mean vector 0 and covariance matrix Σ. Let Ω = Σ−1 = ((ωij))1<=i,j<=p denote the inverse covariance matrix. Denote the sample covariance matrix by S, and the sample corresponding to the ith variable by Yi = (yi 1, yi 2, ... , yi n)'."
My problem is that my data is not normally distributed and the mean is not zero. I don't exactly know what I should do with my data to start. I don't exactly know if I should normalize my data with mean vector 0 and covariance matrix Σ? I don't know what does the article ask me to do for the first step and I don't know exactly how to make sample covariance matrix S. Is there anyone here to give me some notion about the article and what I should do?
edit: The article is here