Parameters estimation using maximum likelihood with fmincon

Hi all,

I need to find the parameters by MLE. My code is as below. It seems to give me the values if without log(L) but incorrect from the original equation.

function LL = Loglikelihood(theta)
   data = readtable('Test_data1.xlsx')
   Gap = data.Var2
   Vni = data.Var3
   an = data.Var4
   pn = data.Var5
   hn = data.Var6
   sn = data.Var7
   n=length(Gap);   %500 samples
   
    b1 = theta(1);  % parameter
    b2 = theta(2);  % parameter
    b3 = theta(3);  % parameter
    b4 = theta(4);  % parameter
    b5 = theta(5);  % parameter
    b6 = theta(6);  % parameter
    sig = theta(7); % sigma
    LL=0;
  %%% try to find log likelihood
  for ind = 1:n    

  L = (1./sig).*(normpdf(((Gap(ind)-(b1.*(Vni(ind).^b2).*((b3).^hn(ind)).*((b4).^pn(ind)).*((b5).^sn(ind))./((abs(an(ind)+exp(-50))).^(b6)))))./(sig)));  
  
   LL= LL+(log(L));
   
  end
   LL = -sum(LL)
end

%%% try to find optimization

  A=[];
  b=[];
  Aeq=[];
  beq=[];
  lb=[-2 -2 0.5 0.5 0.5 -2 0.07];
  ub=[4 4 2 2 2 2 2];
 theta_0 =[ 2 1 1 1.5 1.5 1.5 4 ];
 
 options=optimset('PlotFcns','optimplotfval','Display','off','MaxIter',10000,'TolX', 10e-6, 'MaxFunEvals', 10000, 'TolFun',10e-6);
 [theta,fval,exitflag,output,grad,hessian] = fmincon(@Loglikelihood,theta_0,A,b,Aeq,beq,lb,ub,[],options)
 

The error shows " Error using barrier

Objective function is undefined at initial point". Fmincon cannot continue.

And there are somethings wrong with fmincon function.

Thanks in advance.

[Bjorn Gustavsson]

Since you're using normal-distributed samples the maximum-likelihood estimates should be the identical to the weighted least-squares solution.