I was wondering whether there is something along the lines of a gold-standard to recover a nonparametric estimate of a function $f$ based on observed data $(y_i,x_i)_{i=1}^n$ where the data are known to satisfy $$f(y_i)-\kappa f(x_i)=0$$ Specifically, $f$ is invertible and $\kappa$ is just a (known) real number.
Thanks so much!