Asymptotic distributions for testing dimensionality in q-based pHd

R. Dennis Cook, Xiangrong Yin

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We show that the test statistic for dimension in q-based principal Hessian directions (pHd) is distributed as a linear combination of X2 random variables. Simpler distributions can result depending on the distribution of the predictors and the adequacy of the quadratic model.

Original languageEnglish (US)
Pages (from-to)233-243
Number of pages11
JournalStatistics and Probability Letters
Issue number3
StatePublished - Jul 1 2002

Bibliographical note

Funding Information:
This work was supported in part by National Science Foundation Grant DMS-9703777.

Copyright 2008 Elsevier B.V., All rights reserved.


  • Asymptotic distribution
  • Central subspaces
  • Dimension-reduction subspace
  • Regression graphics
  • pHd


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