Existence and Uniqueness of Semiparametric Projections Applications to Semiparametric Efficiency

Joint with: Ivana Komunjer

In this paper we propose primitive conditions under which a projection of a conditional density onto a set defined by conditional moment restrictions exists and is unique. Moreover, we provide an analytic expression of the obtained projection. Our first result is to show the existence when the moment function is bounded. The result is as we would expect from the analogous results obtained in the unconditional case. Our second result relaxes the boundedness assumption and replaces it with a correct specification condition. Showing that the correct specification of the moment function is sufficient for the projection to exist is entirely new and not yet seen in the literature.

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