how to do mle on custom mvnpdf ?

Hi,

i'm trying to fit two correlated model with MVNpdf.

But it seems that the SIGMA of the function cannot set parameters there

mvnpdf(X,mu,SIGMA)

the model as below

%% S for dr_t
%% L for dl_t
Sx=S(1:end-1);Sy=S(2:end);
Lx=L(1:end-1);Ly=L(2:end);
diffL=Ly-Lx;diffS=Sy-Sx;
func=@(theta) -sum(log(mvnpdf([diffL diffS], ...
                              [theta(1)*(theta(2)-Lx)*delta_t theta(4)*(Lx-Sx)*delta_t], ...
                              [theta(3) theta(6);theta(5) theta(6)])));
param=fminsearch(func,[0.8 0.01 1 0.2 1 0]);

however, i find it doesn't work

it shows "SIGMA must be a square, symmetric, positive definite matrix" and Error in fminsearch.

Is there any solution ? Thanks !!

Answer 1

[Jeff Miller]

I don't really understand what you are trying to do, but the error message "SIGMA must be a square, symmetric, positive definite matrix" suggests the problem. fminsearch is trying different theta values, and sometimes it tries values for which the sigma matrix [theta(3) theta(6);theta(5) theta(6)] is not positive definite.

Inside your error function (not an anonymous one),you will have to compute a legal SIGMA from whatever values fminsearch suggests. (To do that, you may need to re-parameterize the problem a little bit.) For example, fminsearch might try a negative value for theta(3), but variances have to be positive. So, for example, you might have something like

thiscovar = theta(6);
SIGMA(1,1) = abs(theta(3));
SIGMA(1,2) = thiscovar;
SIGMA(2,1) = thiscovar;
SIGMA(2,2) = abs(theta(5));

and then call mvnpdf with this computed SIGMA.