Fast and Robust estimation of the Multivariate Errors in Variables Model

Christophe Croux, Mohammed Fekri, A. Ruiz-Gazen

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

In the multivariate errors in variables models one wishes to re-
trieve a linear relationship of the form y = ¯tx + ®, where both x and y
can be multivariate. The variables y and x are not directly measurable, but
observed with measurement error. The classical approach to estimate the mul-
tivariate errors in variables model is based on an eigenvector analysis of the
joint covariance matrix of the observations. In this paper a projection-pursuit
approach is proposed to estimate the unknown parameters. Focus is on pro-
jection indices based on half-samples. These leads to robust estimators, which
can be computed using fast algorithms. Fisher consistency of the procedure is
shown, without needing to make distributional assumptions on the x-variables.
A simulation study gives insight into the robustness and the e±ciency of the
procedure.
Original languageEnglish
Pages (from-to)286-303
Number of pages18
JournalTest
Volume19
Issue number2
Publication statusPublished - 2010

Keywords

  • Errors in variables
  • Multivariate statistics
  • Principal compo- nents

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