Technical Note—On the Estimation of Convex Functions

We consider the estimation of a convex or concave relationship from a set of limited observations without prior specification of a functional form. A concave programming problem is shown to provide a “best” estimate for an arbitrary norm and n independent variables. The problem is shown to be well suited to a solution using the computational strategy of relaxation (a variant of generalized programming). An example illustrates the procedure and demonstrates the relationship to a procedure for n = 1 suggested by Dent.