A Method of Local Influence Analysis in Sufficient Dimension Reduction

Fei Chen, Lei Shi, Lin Zhu, Lixing Zhu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

A general framework for a local influence analysis is developed for sufficient dimension reduction when the data likelihood is absent and the inference result is a space rather than a vector. A clear and intuitive interpretation of this approach is described. Its application to the sliced inverse regression is presented, together with its invariance properties. A data trimming strategy is also suggested, based on the influence assessment for observations provided by our method. A simulation study and a real-data analysis are presented. The results indicate that the local influence analysis avoids the masking effect, and that the data trimming provides a substantial increase in the inference accuracy.
Original languageEnglish
Pages (from-to)737-753
Number of pages17
JournalStatistica Sinica
Volume32
Issue number2
DOIs
Publication statusPublished - Apr 2022

User-Defined Keywords

  • Central subspace
  • displacement function
  • influence measure
  • perturbation scheme

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