I seem to be having a problem with getting fmincon to solve for the normal log likelihood.
I've generated random numbers with known mean and variance:
t=10000;
xbar = 0.5;
sigmabar = 0.10;
x = xbar + sigmabar*randn(t,1);
I then tried solving for N(muhat, sigmahat^2) using fmincon. I expect that muhat w ill be approximately the same as xbar and sigmahat as sigmabar. To do this, I first write the normal log likelihood as follows
function LL = normlgl(theta,data)
mu = theta(1);
sig = theta(2);
l=-0.5*log(2*pi)-log(sig)-0.5*( (data-mu)/sig ).^2;
LL = sum(l);
Finally, I minimize normlgl using some starting values (theta0) and setting some arbitrary lower and upper bounds.
theta0 = [3;-1];
lb = [-10;0.001];
ub = [10;100];
[thetahat,fval,exitflag] = fmincon('normlgl',theta0,[],[],[],[],lb,ub,[],[],x);
It doesn't seem to work. thetahat is always giving me theta0. I've tried using fminsearch and fminunc without the constraints but that didn't help.
Any ideas?
