Unified predictor hypothesis tests in sufficient dimension reduction: A bootstrap approach

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In this paper, we newly define a unified predictor hypothesis that is applicable to all sufficient dimension reduction (SDR) methodologies. To test the predictor hypothesis, we propose a bootstrap approach by measuring the distances between reference subspaces and bootstrap subspaces. To measure the distances between two subspaces, the vector correlation coefficient is considered. Simulation studies confirm the background reasoning of the proposed tests.

Original languageEnglish
Pages (from-to)217-225
Number of pages9
JournalJournal of the Korean Statistical Society
Issue number2
StatePublished - Jun 2011

Bibliographical note

Funding Information:
For Jae Keun Yoo, this work was supported by a Basic Science Research Program through the National Research Foundation of Korea (KRF) funded by the Ministry of Education, Science and Technology ( 2010-0003189 ). The authors are also grateful to the referees for many helpful comments.


  • Bootstrapping
  • Predictor hypothesis tests
  • Sufficient dimension reduction
  • Vector correlation coefficient


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