I have a problem that I don't think I've met before. I have N observations of the variables v1 and v2 and I assume that there is a function f such as v2 = f(v1).
I want to know if f has a particular 'statistical' monotony (increasing or decreasing) and if it is 'statistically' convex or concave. By 'statistical' I mean that my observations may include error terms so you may encounter pairs of variable that show a monotony that is the opposite of the global monotony, if that's English.
Should I simply compute a f' and a f'' ? (derivatives of f).
If you have some thoughts on this I'd be glad to read it. Thanks,
(btw I use Stata)