AN EQUIVALENCE RESULT FOR VC CLASSES OF SETS
Let and [Theta] be infinite sets and let × [Theta]. 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 [Theta] 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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