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<p>In this note, the authors revisit the envelope dimension reduction, which was first introduced for estimating a sufficient dimension reduction subspace without inverting the sample covariance. Motivated by the recent developments in envelope methods and algorithms, the authors refresh the envelope inverse regression as a flexible alternative to the existing inverse regression methods in dimension reduction. The authors discuss the versatility of the envelope approach and demonstrate the advantages of the envelope dimension reduction through simulation studies.</p>

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Envelope Inverse Regression for Dimension Reduction: A Review and New Perspectives

  • 期刊论文

  • 发表日期：

    2026年2月5日

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  • Jing Zeng,
  • Ning Wang,
  • Xin Zhang

摘要

In this note, the authors revisit the envelope dimension reduction, which was first introduced for estimating a sufficient dimension reduction subspace without inverting the sample covariance. Motivated by the recent developments in envelope methods and algorithms, the authors refresh the envelope inverse regression as a flexible alternative to the existing inverse regression methods in dimension reduction. The authors discuss the versatility of the envelope approach and demonstrate the advantages of the envelope dimension reduction through simulation studies.