SIMEX estimation for single-index model with covariate measurement error

Yiping Yang, Tiejun TONG, Gaorong Li*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

53 Citations (Scopus)


In this paper, we consider the single-index measurement error model with mismeasured covariates in the nonparametric part. To solve the problem, we develop a simulation-extrapolation (SIMEX) algorithm based on the local linear smoother and the estimating equation. For the proposed SIMEX estimation, it is not needed to assume the distribution of the unobserved covariate. We transform the boundary of a unit ball in Rp to the interior of a unit ball in Rp-1 by using the constraint ‖ β‖ = 1. The proposed SIMEX estimator of the index parameter is shown to be asymptotically normal under some regularity conditions. We also derive the asymptotic bias and variance of the estimator of the unknown link function. Finally, the performance of the proposed method is examined by simulation studies and is illustrated by a real data example.

Original languageEnglish
Pages (from-to)137-161
Number of pages25
JournalAStA Advances in Statistical Analysis
Issue number1
Publication statusPublished - 1 Mar 2019

Scopus Subject Areas

  • Analysis
  • Statistics and Probability
  • Modelling and Simulation
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Applied Mathematics

User-Defined Keywords

  • Estimating equation
  • Local linear smoother
  • Measurement error
  • Single-index model


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