Overlapped groupwise dimension reduction

Jing Ke Zhou, Jian Rong Wu, Lixing ZHU*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

Existing groupwise dimension reduction requires given group structure to be non-overlapped. This confines its application scope. We aim at groupwise dimension reduction with overlapped group structure or even unknown group structure. To this end, existing groupwise dimension reduction concept is extended to be compatible with overlapped group structure. Then, the envelope method is ameliorated to deal with overlapped groupwise dimension reduction. As an application, Gaussian graphic model is employed to estimate the structure between predictors when the group structure is not given, and the amended envelope method is used for groupwise dimension reduction with graphic structure. Furthermore, the rationale of the proposed estimation procedure is explained at the population level and the estimation consistency is proved at the sample level. Finally, the finite sample performance of the proposed methods is examined via numerical simulations and a body fat data analysis.

Original languageEnglish
Pages (from-to)2543-2560
Number of pages18
JournalScience China Mathematics
Volume59
Issue number12
DOIs
Publication statusPublished - 1 Dec 2016

Scopus Subject Areas

  • Mathematics(all)

User-Defined Keywords

  • envelope method
  • Gaussian graphic model
  • groupwise dimension reduction
  • overlapped group structure
  • sufficient dimension reduction

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