Nonparametric Estimation of Nonadditive Random Functions

We present estimators for nonparametric functions that depend on unobservable random variables in nonadditive ways. The distributions of the unobservable random terms are assumed to be unknown. We show how properties that may be implied by economic theory, such as monotonicity, homogeneity of degree one, and separability can be used to identify the unknown, nonparametric functions and distributions. We also present convenient normalizations, to use when the properties of the functions are unknown. The estimators for the nonparametric distributions and for the nonparametric functions and their derivatives are shown to be consistent and asymptotically normal. The results of a limited simulation study are presented.