A data-adaptive hybrid method for dimension reduction

Li Ping Zhu*, Lixing ZHU

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

To gain the advantages of different inverse regression methods, the convex combination can be useful for estimating the central subspace. To select an appropriate combination coefficient in the hybrid method, we propose in this paper a data-adaptive hybrid method using the trace of kernel matrices. For ease of illustration, we consider particularly the combination of inverse regressions using the conditional mean and the conditional variance, both of which are separately powerful in estimating different models. Because the efficacy of the slicing estimation may deteriorate when it is used to estimate the conditional variance, we use the kernel smoother instead. The asymptotic normality at the root-n rate is achieved even with the data-driven combination weight. Illustrative examples by simulations and an application to horse mussel data is presented to demonstrate the necessity of the hybrid models and the efficacy of our kernel estimation.

Original languageEnglish
Pages (from-to)851-861
Number of pages11
JournalJournal of Nonparametric Statistics
Volume21
Issue number7
DOIs
Publication statusPublished - Oct 2009

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • Asymptotic normality
  • Central subspace
  • Dimension reduction
  • Inverse regression

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