AN EQUIVALENCE RESULT FOR VC CLASSES OF SETS

Scott Joslin and Robert P. Sherman

Econometric Theory, 2003, vol. 19, issue 06, pages 1123-1127

Abstract: Let and be infinite sets and let . 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 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.

Date: 2003

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