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Published December 1, 2003 | public
Journal Article Open

An equivalence result for VC classes of sets


Let R and θ be infinite sets and let A # R × θ. We show that the class of projections of A onto R 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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Copyright © 2003 Cambridge University Press. Reprinted with permission. Published online by Cambridge University Press 24 September 2003


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