[julia-users] Computing Standard Error for MLE using Optim package

[Bradley Fay]

I'm trying to figure out how to compute/recover the standard error of the 
estimates for a simple linear regression using MLE and simulated. Here is 
the code I'm using to generate data, compute the likelihood function, and 
optimize the function.

using Optim

using Distributions


xmat = [ones(10000,1) rand(Normal(2,1),10000)]; #creating matrix of Independent 
varibles

u = rand(Normal(0,1),10000); #create vector of normally distributed errors mean 
0 std 1

ymat = xmat*[3,2] + u; #generating dependent variables.


start_val = [1.0,1.0,1.0]; #Starting values for MLE estimation. Need to be in 
float format.


#Beginning of Likelihood function

function ll(param);

        b1=param[1];

        b2=param[2];

        sig=param[3];   
        ee =  ymat-xmat*[b1,b2];

        loglik = -0.5*log(2*pi*sig^2)-0.5*(ee.^2)/sig^2;

        -sum(loglik);

end;


optimize(ll,start_val)


I'm more familiar with Gauss and MATLAB as I just started playing with 
Julia yesterday. To compute the standard errors in the identical situation 
in MATLAB, I can directly compute the square root of the diagonal of the 
inverse of the numerical hessian because Matlab will return the hessian.
mlese=sqrt(diag(inv(hessian))); #MATLAB Code for computing standard errors

Is there a way to do this in Julia? I'm having trouble figuring this out. 
 Thanks!