Asymptotics for kernel estimation of slicing average third-moment estimation

Li Ping Zhu*, Lixing ZHU

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

To estimate central dimension-reduction space in multivariate nonparametric regression, Sliced Inverse Regression[7] (SIR), Sliced Average Variance Estimation[4] (SAVE) and Slicing Average Third-moment Estimation[14] (SAT) have been developed. Since slicing estimation has very different asymptotic behavior for SIR and SAVE, the relevant study has been made case by case, when the kernel estimators of SIR and SAVE share similar asymptotic properties. In this paper, we also investigate kernel estimation of SAT. We prove the asymptotic normality, and show that, compared with the existing results, the kernel smoothing for SIR, SAVE and SAT has very similar asymptotic behavior.

Original languageEnglish
Pages (from-to)103-114
Number of pages12
JournalActa Mathematicae Applicatae Sinica
Volume22
Issue number1
DOIs
Publication statusPublished - Jan 2006

Scopus Subject Areas

  • Applied Mathematics

User-Defined Keywords

  • Asymptotic normality
  • Bandwidth selection
  • Dimension reduction
  • Inverse regression method
  • Kernel estimation

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