R help - Dec 2003 - smoothing functions

Dear all,

I am trying to program an estimator which maximizes a likelihood type 
objective function which is basically just lots of sums of indicator 
functions of data and parameters. In order to make the optimization I 
would like to smooth these functions. Since they are either 0 or 1, one 
possibility is to use the normal cdf.

I am wondering whether anyone is aware of a less arbitrary choice of a 
smoothing function? (is there any theory that suggests what's best to 
use?) Does anyone have any recommendations on what works best numerically?

Thanks, Eugene.

Eugene  -

Is the estimand in your problem (the parameter which you seek
to estimate) discrete-valued or continuous-valued ?  If it is
discrete-valued, then you are heading in the wrong direction,
because no matter how smooth you make the objective function,
you will not be able to differentiate it with respect to the
parameter !   I think I don't have quite enough information
to give a helpful answer to your question  . . .  but more
important is for you to find the answer yourself.

-  tom blackwell  -  u michigan medical school  -  ann arbor  -

On Mon, 1 Dec 2003, Eugene Salinas (R) wrote:
> Dear all,
>
> I am trying to program an estimator which maximizes a likelihood type
> objective function which is basically just lots of sums of indicator
> functions of data and parameters. In order to make the optimization I
> would like to smooth these functions. Since they are either 0 or 1, one
> possibility is to use the normal cdf.
>
> I am wondering whether anyone is aware of a less arbitrary choice of a
> smoothing function? (is there any theory that suggests what's best to
> use?) Does anyone have any recommendations on what works best numerically?
>
> Thanks, Eugene.
>
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