why mvnrnd works with a singular covariance matrix
in [Matlab]
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From: Farzin Zareian on 11 May 2010 23:23 Hi Roger Its great to be guided by an UCI alumnus. Many thanks for your detailed response. I can totally understand the situation and the large level of uncertainty in my estimates. I have no choice other than assuming that my seven variables are joint normal. I will try to dig into the literature to see if I can find a measure by which I can quantify the level of uncertainty for the joint normal distribution parameters estimates. Please drop me a line if anything comes to your mind. I will post my findings here for other's reference. best farzin
From: Greg Heath on 12 May 2010 04:56
On May 11, 11:23 pm, "Farzin Zareian" <zare...(a)uci.edu> wrote: > Hi Roger > > Its great to be guided by an UCI alumnus. Many thanks for your detailed response. > > I can totally understand the situation and the large level of uncertainty in my estimates. I have no choice other than assuming that my seven variables are joint normal. > > I will try to dig into the literature to see if I can find a measure by which I can quantify the level of uncertainty for the joint normal distribution parameters estimates. Please drop me a line if anything comes to your mind. > > I will post my findings here for other's reference. Most of my successful simulations based on Gaussian distributions tend to have an observation to estimated parameter ratio that exceeds 13, i.e. , for each Gaussian Nobs = ceil(r*Np) for r >~13 where Np = n+n*(n+1)/2 Typically r ~ 30 tends to be sufficient for the amount of precision that I require. If you want to get something more reliable, go to the statistics handbooks to find expressions for the standard deviation of estimates for means, variances, and correlation coefficients given that the joint distribution is Gaussian. Hope this helps. Greg |