A sparse eigen-decomposition estimation in semiparametric regression

Li Ping Zhu, Zhou Yu, Lixing ZHU*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

Abstract

For semiparametric models, one of the key issues is to reduce the predictors' dimension so that the regression functions can be efficiently estimated based on the low-dimensional projections of the original predictors. Many sufficient dimension reduction methods seek such principal projections by conducting the eigen-decomposition technique on some method-specific candidate matrices. In this paper, we propose a sparse eigen-decomposition strategy by shrinking small sample eigenvalues to zero. Different from existing methods, the new method can simultaneously estimate basis directions and structural dimension of the central (mean) subspace in a data-driven manner. The oracle property of our estimation procedure is also established. Comprehensive simulations and a real data application are reported to illustrate the efficacy of the new proposed method.

Original languageEnglish
Pages (from-to)976-986
Number of pages11
JournalComputational Statistics and Data Analysis
Volume54
Issue number4
DOIs
Publication statusPublished - 1 Apr 2010

Scopus Subject Areas

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

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