Problem in estimating MLE with 'fimincon' function

Hello,

I recently started using Matlab and got stuck in a problem.

I am trying to verify that OLS estimators are same as those under the method of MLE under usual basic assumptions.

So I first made up a specification equation like below,

function [ fvale,gradf ] = lognormlike(w)

a= randn(1000,2); z = a(:,1); e = a(:,2); %date vector y = 2+3*z + e; <-----this is my equation I want to test. x = [ones(1000,1) z]; beta = [w(1);w(2)]; e2 = y - x*beta; [n,l] = size(x);

fvale = sum(log(normpdf(e2,0,w(3)))); gradf = [(w(3)^(-2))*x'*e2; (-1)*n/(2*w(3)^2) + ((2*w(3)^4)^(-1)) * e2'*e2];

end

I had no problem when I put some vector in my 'lognormlike'function. So I took the next step.

Maximization

w0 = [4,1,2]; options = optimset('GradObj','on','LargeScale','on','Display','off'); [w,fval] = fmincon(@lognormlike,w0,[],[],[],[],[-100,-100,1],[100,100,100],[],options);

Here above is my simple maximization program using 'fimincon' function, and the problme popped up.

First, when I did run this program without 'GradObj', it said it needed gradient. So, I added. But When I added gradient and ran, it said like this,

'Warning: Your current settings will run a different algorithm (interior-point) in a future release. > In fmincon at 874 In norm_mle at 3 '

And every time I did run this program, it gave me different answer. I changed low bound and upper bound, but it did not fix the problem.(but value changed)

And When I did run this with 'Largescale off', it keeps giving me anwer whose value is same as initial value. I think I have some problme in choosing the algorithm for optimizaing, but I don't know where exactly I took a mistake.

One more, is there any method I can solve this problme with 'mle' built-in function? I mean when I have parametor in data, just like 'e2'.

It would be very helpful to me if you give an answer to my question since this is driving me crazy right now.........