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st: optimization in mata but unique obj function


From   "Abhimanyu Arora" <abhimanyu.arora@student.kuleuven.be>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: optimization in mata but unique obj function
Date   Thu, 15 Apr 2010 11:07:45 +0200

Dear statalist
This problem has not been addressed in the manuals (though there was an
entry by in the statalist by Bob Hammond some time ago that came a bit close
to it). So only your experience could help.

The problem is the following-
I need to estimate parameters by maximizing the likelihood function.
 
There are two features of this function:

(1) The function depends on the value of the observation in the following
sense. Eg for x=1 L(x,theta)=ax, for x=2 L(x,theta)=bx.

(2) Also included in the likelihood function is a function of parameters to
be estimated (in other words a,b are functions of theta (vector))

Hitherto, I was using mata's optimize function- as I create my parameter
function, referred in (2) in mata [(2) is also the reason for not using ml
commands]

The v0 evaluator would have served my purpose but it seems to have the
following shortcoming: the form of the function has to be the same for all
observations (pg 287-288 of the mata manual).


How I tried to go about it
***************************

I have my data as a matrix in mata , let's say 1000X1.

After my void evaluator command,

I create a loop (using for(i=1;i<1000;i++) 

I use the if x[i]==....
          V=F(x[i])...
And have a set of statements like these depending on values taken by x[i],V
being my likelihood function (and F varies according to x[i] 

And use the necessary optimizing commands

(And stata doesn't report error, neither does it gives estimates)

Why I know this is not correct    
******************************  
I replicate the example in the mata manual (pg 288) (or first example of
v0,v1,v2 in the online help for optimize) but which I use the for loop
(i=1;i<11;i++) and use x[i] in place of x (adding removing ":" doesn't make
a difference). And voila! I do not get the parameter estimates (should have
got 3.71, 7.01 had it been ok).




Hence the question is -while stata seems to take care of (1) as we can use
our -if-qualifier in our likelihood evaluator, mata can address (2), but how
can we take both into account?



I hope the problem is not as difficult for you as it has been for me. 

Thank you very much for going through this long email.
Best regards
Abhimanyu Arora
KU Leuven

  

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