THE LIMITS OF ECONOMETRICS: NONPARAMETRIC ESTIMATION IN HILBERT SPACES
计量经济学的边界:Hilbert 空间中的非参数估计
We extend Bergstrom's 1985 results on nonparametric (NP) estimation in Hilbert spaces to unbounded sample sets. The motivation is to seek the most general possible framework for econometrics, NP estimation with no a priori assumptions on the functional relations nor on the observed data. In seeking the boundaries of the possible, however, we run against a sharp dividing line, which defines a necessary and sufficient condition for NP estimation. We identify this condition…