I am trying to fit a K-dimensional multivariate gaussian distribution (ie. learn mu and Sigma) from data missing completely at random. On the internet, I have found unbiased solutions via EM, as well as a few older, fairly complicated methods. I am curious if anyone knows why "the obvious solution" is never mentioned. By the "obvious solution" I mean simply taking the mean of all observed entries (to learn mu), & the correlation amongst observed pairs of variables, and the variance of individual variables (to learn Sigma).
Thanks in advance!