topic Re: high values of MLE in SAS/IML Software and Matrix Computations

high values of MLE

Salah — Tue, 29 Jul 2025 19:06:47 GMT

I am working on a very simple problem that I have addressed several times before, and I always receive good estimates. For some reason, this time I am failing miserably; the maximum likelihood estimates (MLE) are so HUGE. I’m not sure where I went wrong. I need help, please.

Proc iml;
seed=0;   	theta= 1.5 ; 	beta= 1;   		 m=50;     			      
print theta beta m ;

**** MLE ***;
 start MLE_func(y) global (m,X);
	 func=0;
	 theta=y[1];
	 beta=y[2];		 
	 Log_X=log(1+x#beta);
	 func=func + m*log(theta*beta) - (theta+1) * Log_X[+] ;
         Return(func);
 finish;

call randseed(seed);                         
call randgen(U, "Uniform"); 
Call sort(U);
X =(  (1-U)##(-1/theta) - 1  )/ beta;

************* Constrain MLE ***********************;
con={.001 .001, . .  };
x0={1,1};
opt={2 0};
tc={10000 16000};
Call  nlpqn(rc, MLE_ret, "MLE_func", x0, opt, con,tc);

Theta_hat = MLE_ret[1];
Beta_hat  = MLE_ret[2];
print Theta_hat  Beta_hat;
quit;

Thank you

Re: high values of MLE

Rick_SAS — Tue, 29 Jul 2025 19:05:29 GMT

When posting an example, please use a seed value that is nonzero so that we can reproduce your results. In the following, I use
seed=10;

You can't perform a MLE on a single datum. You need a sample size greater than 1. I suspect you know this and just forgot to allocate an array for U. This should address your immediate problem:

Proc iml;
seed=10;   	theta= 1.5 ; 	beta= 1;   		 m=50;     			      
print theta beta m ;

**** MLE ***;
start MLE_func(y) global (m,X);
 theta=y[1];
 beta=y[2];
 Log_X=log(1+x#beta);
 func = m*log(theta*beta) - (theta+1) * Log_X[+] ;
 Return(func);
finish;

call randseed(seed);    
N = 100;
U = j(N, 1); 
call randgen(U, "Uniform"); 
Call sort(U);
X =(  (1-U)##(-1/theta) - 1  )/ beta;

************* Constrain MLE ***********************;
x0={1,1};
con={.001 .001, . .  };
opt={2 0};
tc={10000 16000};
Call  nlpqn(rc, MLE_ret, "MLE_func", x0, opt, con,tc);

Theta_hat = MLE_ret[1];
Beta_hat  = MLE_ret[2];
print Theta_hat  Beta_hat;

Re: high values of MLE

Salah — Wed, 30 Jul 2025 12:39:58 GMT

Thank you so much!!!

Re: high values of MLE

Rick_SAS — Tue, 05 Aug 2025 13:28:14 GMT

Do you need any further help? If not, you can close this thread.

Re: high values of MLE

Salah — Tue, 05 Aug 2025 13:33:53 GMT

I am sorry, I thought that I closed it by just hitting the thumb up.