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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