Necessary and sufficient conditions for consistency of A method for smoothed functional inverse regression

R. D. Cook, L. Forzani, A. F. Yao

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

Ferré and Yao (2005, 2007) proposed a method to estimate the Effective Dimension Reduction space in functional sliced inverse regression. Their approach did not require the inversion of the variance-covariance operator of the explanatory variables, and it allowed them to get √n consistent estimators in the functional case. In those papers there is a mistake. In this note we show that, in general, the approach does not give an estimator of the SIR subspace. We also give necessary and sufficient conditions for this to be true.

Original languageEnglish (US)
Pages (from-to)235-238
Number of pages4
JournalStatistica Sinica
Volume20
Issue number1
StatePublished - Jan 2010

Keywords

  • Dimension reduction
  • Functional data analysis
  • Inverse regression

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