WIAS Preprint No. 999, (2004)

SIMEX and TLS: An equivalence result



Authors

  • Polzehl, Jörg
    ORCID: 0000-0001-7471-2658
  • Zwanzig, Silvelyn

2010 Mathematics Subject Classification

  • 62F12 62J05

Keywords

  • Errors-in-variables, SIMEX, Moment estimator, Total Least Squares

Abstract

SIMEX was introduced by Cook and Stefanski (1994) as a simulation type estimator in errors-in-variables models. The idea of the SIMEX procedure is to compensate for the effect of the measurement errors while still using naive regression estimators. Polzehl and Zwanzig (2004) defined a symmetrized version of this estimator. In this paper we establish some results relating these two simulation-extrapolation-type estimators to well known consistent estimators like the total least squares estimator (TLS) and the moment estimator (MME) in the context of errors-in-variables models. We further introduce an adaptive SIMEX (ASIMEX), which is calculated like SIMEX, but based on an estimated variance. The main result of this paper is that SYMEX, ASIMEX are equivalent to TLS. Additionally we see that SIMEX is equivalent to the moment estimator.

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