I have been searching the internet for a generalized method for doing regression analysis on non linear data. My model can be represented as
$$Y = \beta_0f(X_0) + \beta_1g(X_1) + ... + \beta_nz(X_n) + \varepsilon$$
where I don't have any idea what $f() g() z()$ are. But I can constrict myself to a domain saying that
$$f(), g(), z(), \varepsilon \in [\sin(), \log(), x^2, x^3, 1/x, e^x, x] $$
Please forgive me for any terminology mistake, I mean $f(), g(), h()$ can be one of the functions given in that set.
I've researched that once we know the equation, in certain cases we can linearize it so the form becomes linear regression. Is there no way to do a regression analysis for this form then? Without knowing the equation itself?
I'm a better programmer than a statistician and so I'm not averse to taking an iterative approach substituting the functions in each stage as long as someone can please guide me through the iterative process.
Further, isn't this model more frequently encountered in real life? I haven't seen any examples of this at all on the web.