Response dimension reduction: model-based approach

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Abstract

In this paper, a model-based approach to reduce the dimension of response variables in multivariate regression is newly proposed, following the existing context of the response dimension reduction developed by Yoo and Cook [Response dimension reduction for the conditional mean in multivariate regression. Comput Statist Data Anal. 2008;53:334–343]. The related dimension reduction subspace is estimated by maximum likelihood, assuming an additive error. In the new approach, the linearity condition, which is assumed for the methodological development in Yoo and Cook (2008), is understood through the covariance matrix of the random error. Numerical studies show potential advantages of the proposed approach over Yoo and Cook (2008). A real data example is presented for illustration.

Original languageEnglish
Pages (from-to)409-425
Number of pages17
JournalStatistics
Volume52
Issue number2
DOIs
StatePublished - 4 Mar 2018

Keywords

  • Envelope
  • Grassmann manifold
  • multivariate regression
  • response dimension reduction
  • sufficient dimension reduction

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