Nonparametric estimation of homogeneous function

Consider the regression y = f(x) + e ' where E (e | x) = 0 and the exact functional form of f is unknown, although we do know that it is homogeneous of known degree r. Using a local linear approach we examine two ways of nonparametrically estimating f: (i) a direct or numeraire approach, and (ii) a projection based approach. We show that depending upon the nature of the conditional variance var (E | x), one approach may be asymptotically better than the other. Results of a small simulation experiment are presented to support our findings.