On model-free conditional coordinate tests for regressions

Zhou Yu*, Lixing ZHU, Xuerong Meggie Wen

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

4 Citations (Scopus)


Existing model-free tests of the conditional coordinate hypothesis in sufficient dimension reduction (Cook (1998). [3]) focused mainly on the first-order estimation methods such as the sliced inverse regression estimation (Li (1991). [14]). Such testing procedures based on quadratic inference functions are difficult to be extended to second-order sufficient dimension reduction methods such as the sliced average variance estimation (Cook and Weisberg (1991). [9]). In this article, we develop two new model-free tests of the conditional predictor hypothesis. Moreover, our proposed test statistics can be adapted to commonly used sufficient dimension reduction methods of eigendecomposition type. We derive the asymptotic null distributions of the two test statistics and conduct simulation studies to examine the performances of the tests.

Original languageEnglish
Pages (from-to)61-72
Number of pages12
JournalJournal of Multivariate Analysis
Publication statusPublished - Aug 2012

Scopus Subject Areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • Conditional coordinate test
  • Sliced inverse regression
  • Sufficient dimension reduction


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