Econometric Theory



MISCELLANEA

AN EQUIVALENCE RESULT FOR VC CLASSES OF SETS


Scott  Joslin  a1 c1 and Robert P.  Sherman  a2
a1 Stanford University
a2 California Institute of Technology

Article author query
joslin s   [Google Scholar] 
sherman rp   [Google Scholar] 
 

Abstract

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.


Correspondence:
c1 Address correspondence to: Scott Joslin, Stanford Graduate School of Business, 518 Memorial Way, Stanford University, Stanford, CA 94305-5015, USA; e-mail: sherman@hss.caltech.edu.


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