T-stats of max, when Hessian is not invertable?

deleted_user — Mon, 23 Jun 2008 17:58:57 GMT

I have the following function I would like to find the Maximum Likelihood Estimates for alpha1, alpha2, sigma_r, and sigma_n:

SS = sqrt(sigma_r^2+sigma_n^2);
PP = sigma_r*sigma_n;

A = {cdf(('NORMAL',(-alpha2+Ret*sigma_r^2/SS^2)*SS/PP,0,1) + cdf('NORMAL',(-alpha1-Ret*sigma_r^2/SS^2)*SS/PP,0,1)}*pdf('NORMAL',Ret/SS,0,1)/SS;
B = {cdf('NORMAL',alpha2/sigma_r,0,1)-cdf('NORMAL',-alpha1/sigma_r,0,1)}*pdf('NORMAL',Ret/sigma_n,0,1)/sigma_n;

Min -log(A+B);

However the Hessian is singlular. I don't know how to get t-stats. Can anyone tell me, step-by-step (preferably with SAS code), how to find the MLEs and corresponding t-stats or p-values for this problem... using SAS?

"Ret" is the time-series of the return on a stock or a group of stocks.

Thanks so much,

Steve

topic T-stats of max, when Hessian is not invertable? in Mathematical Optimization, Discrete-Event Simulation, and OR

T-stats of max, when Hessian is not invertable?