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Biometrika Advance Access first published online on August 5, 2007
This version published online on August 8, 2007
Biometrika, doi:10.1093/biomet/asm055
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Copyright © 2007 Biometrika Trust

Article

Implications of influence function analysis for sliced inverse regression and sliced average variance estimation

Luke A. Prendergast

Department of Mathematics and Statistics, La Trobe University, Melbourne 3086, Australia

luke.prendergast{at}latrobe.edu.au

Received for publication 1 May 2006. Revision received 1 February 2007.
  Abstract

Sliced inverse regression, sliced inverse regression II and sliced average variance estimation are three related dimension-reduction methods that require relatively mild model assumptions. As an approximation for the relative influence of single observations from large samples, the influence function is used to compare the sensitivity of the three methods to particular observational types. The analysis carried out here helps to explain why there is a lack of agreement concerning the preferability of these dimension-reduction procedures in general. An efficient sample version of the influence function is also developed and evaluated.

Key Words: Bénasséni's coefficient • Dimension reduction • Influence function • Robustness • Sliced average variance estimation • Sliced inverse regression


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