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AN EQUIVALENCE RESULT FOR VC CLASSES OF SETS

Published online by Cambridge University Press:  24 September 2003

Scott Joslin
Affiliation:
Stanford University
Robert P. Sherman
Affiliation:
California Institute of Technology

Abstract

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.

Type
MISCELLANEA
Copyright
© 2003 Cambridge University Press

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