Nonlinear models with measurement errors subject to single-indexed distortion

Jun Zhang, Lixing ZHU, Hua Liang*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

36 Citations (Scopus)


We study nonlinear regression models whose both response and predictors are measured with errors and distorted as single-index models of some observable confounding variables, and propose a multicovariate-adjusted procedure. We first examine the relationship between the observed primary variables (observed response and observed predictors) and the confounding variables by appropriately estimating the single index. We then develop a semiparametric profile nonlinear least square estimation procedure for the parameters of interest after we calibrate the error-prone response and predictors. Asymptotic properties of the proposed estimators are established. To avoid estimating the asymptotic covariance matrix that contains the infinite-dimensional nuisance distorting functions and the single index, and to improve the accuracy of the proposed estimation, we also propose an empirical likelihood-based statistic, which is shown to be asymptotically chi-squared. A simulation study is conducted to evaluate the performance of the proposed methods and a real dataset is analyzed as an illustration.

Original languageEnglish
Pages (from-to)1-23
Number of pages23
JournalJournal of Multivariate Analysis
Publication statusPublished - Nov 2012

Scopus Subject Areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • Covariate-adjusted regression
  • Distorting function
  • Empirical likelihood
  • Error-prone
  • Estimating equation function
  • Local linear smoothing
  • Measurement errors models
  • Single index


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