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Biometrika Advance Access originally published online on May 13, 2007
Biometrika 2007 94(2):496-501; doi:10.1093/biomet/asm029
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Copyright © 2007 Biometrika Trust

Miscellanea

Identifiability of single-index models and additive-index models

Wei Lin

Department of Mathematics, Ohio University, Athens, Ohio 45701, U.S.A.

K. B. Kulasekera

Department of Mathematical Sciences, Clemson University, Clemson, South Carolina 29631, U.S.A.

linwei{at}math.ohiou.edu

kk{at}clemson.edu

Received for publication 1 March 2006. Accepted for publication 1 September 2006.


  Abstract

We provide a proof for the identifiability for both single-index models and partially linear single-index models assuming only the continuity of the regression function, a condition much weaker than the differentiability conditions assumed in the existing literature. Our discussion is then extended to the identifiability of the additive-index models.

Key Words: Additive multiple-index model • Identifiability • Partially linear single-index model • Single-index model


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