# multivariate normal distribution with mean vector 0 and covariance matrix Σ

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

• What is "the article" to which you are referring? It doesn't seem to have much to do with regression and nothing to do with multivariate regression. – whuber Dec 8 '18 at 22:48
• @whuber I added the article – Sara Dec 9 '18 at 9:39
• It might help if you described not the article so much as what your data is and what you want to do with it. The article is probably not a good starting point without a lot of background, and there may be simpler things that you can do. – Carl Dec 9 '18 at 10:57
• Welcome to CV. That doesn't seem like an article that you want to be using to learn regression. Have you had a course in regression? Or have you read an introductory book? Also, are you sure you mean "multivariate" and not "multiple" regression? (The former refers to having multiple dependent variables and is not a beginner topic). – Peter Flom Dec 9 '18 at 11:37
• Dear @PeterFlom I had a course on regression but not a multivariate one. I have no problem with running regression and I have completely written the code to run regression on my data but I have problem with the sentences written in the article that I have mentioned above. I don't exactly know how to change my data to be completely ready for starting regression. As I mentioned, my data is not normal and as mentioned in the article the random vector Yk denote iid observations from a multivariate distribution with mean vector 0 and covariance matrix Σ – Sara Dec 9 '18 at 11:43