maximum likelihood estimation with fminsearch

Hello, I would like to do a maximum likelihood estimation of normal function with the help of fminsearch. It is already working when I dont have any constraints for mu and sigma. I get the estimated mu, sigma and its value of the likelihood function. However, i will fix mu=0 but the resulting mu is never exactly 0 at the end. I dont understand why and in wich way i could do it better.

My code:

first_guess=[0 2];

[Mu_Sigma,Lk] = fminsearch('nlglklySACCzeroMu',first_guess,data);

MuEstimate(2) = Mu_Sigma(1);

SigmaEstimate(2) = Mu_Sigma(2);

L(2)=Lk;

---- next function

function L = nlglklySACCzeroMu(guess)

global data;

guess(1)=0;

if guess(2) < 0

  L = inf;

else

      l=-0.5*log(2*pi)-log(guess(2))-0.5*( data/guess(2) ).^2;

      L = -sum(l);

end

I would be very glad to receive some suggestions! Julia

Answer 1

[Matt J]

If you are fixing mu=0, your function should depend on only one unknown (sigma), not two.

[Julia]

0 and 2 are the parameters to start fminsearch. They will change within every iteration.

[Matt J]

You shouldn't be asking fminsearch to solve for 2 unknowns if you say that mu is fixed. mu should not be treated as an unknown at all if you already know that mu=0.

[Julia]

i got it :-D I dont have to give fminsearch two startparameters! thank you!

[mohanish]

what is the code you used to find the maximum likelihood ratio?