[R] fitting a curve according to a custom loss function

Vadim Ogranovich vograno at arbitrade.com
Wed Feb 19 00:35:44 CET 2003

Dear R-Users,

I need to find a smooth function f() and coefficients a_i that give the best
fit to

y ~ a_0 + a_1*f(x_1) + a_2*f(x_2)

Note that it is the same non-linear transformation f() that is applied to
both x_1 and x_2.

So my first question is how can I do it in R?

A more general question is this: suppose I have a utility function U(a_i,
f()), where f() is say a spline. Is there a general optimizer that could
find an extremum of such U()? If not, how easy it would be to hack up
something like this? Would it become easier if U() depended on f() only,
i.e. no a_i terms?

Thanks, Vadim

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