Groupwise dimension reduction

Lexin Li*, Bing Li, Lixing ZHU

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

38 Citations (Scopus)


In many regression applications, the predictors fall naturally into a number of groups or domains, and it is often desirable to establish a domain-specific relation between the predictors and the response. In this article, we consider dimension reduction that incorporates such domain knowledge. The proposed method is based on the derivative of the conditional mean, where the differential operator is constrained to the form of a direct sum. This formulation also accommodates the situations where dimension reduction is focused only on part of the predictors; as such it extends Partial Dimension Reduction to cases where the blocked predictors are continuous. Through simulation and real data analyses, we show that the proposed method achieves greater accuracy and interpretability than the dimension reduction methods that ignore group information. Furthermore, the new method does not require the stringent conditions on the predictor distribution that are required by existing methods.

Original languageEnglish
Pages (from-to)1188-1201
Number of pages14
JournalJournal of the American Statistical Association
Issue number491
Publication statusPublished - Sept 2010

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • Central mean subspace
  • Direct sum of differential operators
  • Minimum average variance estimation
  • Outer product estimator
  • Partial dimension reduction


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