local interpolation

[FernandoRios]

Dear Statalisters
I was wondering if anyone has written or knows of a function that obtains the best interpolation based on two series where we know that one is a smooth transformation of the other.
Say, for example, that y=F(X), we do not know F, but we know its an strictly increasing and Smooth function so that every value of X is paired with a unique value of Y.
What i need know is that given that i have the data for Y and X, i can obtain the "correct" y for any value X of my choice.
To be more concrete. see the example below

sysuse auto, clear
gen lnprice=ln(price)
sum lnprice
gen Fprice=normal((lnprice-r(mean))/r(sd))
* now we know that there is a smooth and unknown function F that transforms price into Fprice.
* Now, how do I obtain the best interpolation of Fprice for, say, price=5000?

Suggestions are appreciated.
Thank you

[Liu Qiang]

hi Fernando, could mipolate (SSC package) help? I have no deep investigation into this command but in my opinion, given the function form is unknown, if you wanna predict y at a certain x, the best way is to borrow the nearest observations.
Best Wishes

[FernandoRios]

I think that does something else that i also needed. Thank you Liu!