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Let
and Θ be infinite sets and let
× Θ. We show that the class of projections of A onto
is a Vapnik–Chervonenkis (VC) class of sets if and only if
the class of projections of A onto Θ is a VC class.
We illustrate the result in the context of semiparametric estimation of a
transformation model. In this application, the VC property is hard
to establish for the projection class of interest but easy to establish for
the other projection class.
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