Partial linear single index models with distortion measurement errors

Jun Zhang, Yao Yu, Lixing ZHU, Hua Liang*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

32 Citations (Scopus)


We study partial linear single index models when the response and the covariates in the parametric part are measured with errors and distorted by unknown functions of commonly observable confounding variables, and propose a semiparametric covariate-adjusted estimation procedure. We apply the minimum average variance estimation method to estimate the parameters of interest. This is different from all existing covariate-adjusted methods in the literature. Asymptotic properties of the proposed estimators are established. Moreover, we also study variable selection by adopting the coordinate-independent sparse estimation to select all relevant but distorted covariates in the parametric part. We show that the resulting sparse estimators can exclude all irrelevant covariates with probability approaching one. A simulation study is conducted to evaluate the performance of the proposed methods and a real data set is analyzed for illustration.

Original languageEnglish
Pages (from-to)237-267
Number of pages31
JournalAnnals of the Institute of Statistical Mathematics
Issue number2
Publication statusPublished - Apr 2013

Scopus Subject Areas

  • Statistics and Probability

User-Defined Keywords

  • Coordinate-independent sparse estimation (CISE)
  • Covariate adjusted
  • Dimension reduction
  • Distorting function
  • Measurement errors
  • Minimum average variance estimation (MAVE)
  • Single index
  • Sparse principle component (SPC)


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