I'm not sure but PROC UNIVARIATE may only give you the maximum likelihood estimators.
How could you optimize by mean square errors? The F(xi) in your equation is unknown.
Anyway, no matter what you want to optimize, you can program step by step using [url=http://support.sas.com/onlinedoc/913/getDoc/en/imlug.hlp/langref_sect176.htm:39e8ho1z]Nonlinear Optimization and Related Subroutines[/url:39e8ho1z].
Above all, my level is low and don't just take whatever I said.