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AN EQUIVALENCE RESULT FOR VC CLASSES OF SETS

Published online by Cambridge University Press:  24 September 2003

Scott Joslin  and
Robert P. Sherman
Scott Joslin
Affiliation:
Stanford University
Robert P. Sherman
Affiliation:
California Institute of Technology
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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
Information
Econometric Theory , Volume 19 , Issue 6 , December 2003 , pp. 1123 - 1127
Copyright
© 2003 Cambridge University Press

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