Partial linear single index models with distortion measurement errors

Jun Zhang, Yao Yu, Li-Xing Zhu and Hua Liang ()

Annals of the Institute of Statistical Mathematics, 2013, vol. 65, issue 2, 237-267

Abstract: 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. Copyright The Institute of Statistical Mathematics, Tokyo 2013

Keywords: Coordinate-independent sparse estimation (CISE); Covariate adjusted; Dimension reduction; Distorting function; Minimum average variance estimation (MAVE); Measurement errors; Single index; Sparse principle component (SPC) (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (9)

Downloads: (external link)
http://hdl.handle.net/10.1007/s10463-012-0371-z (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:aistmt:v:65:y:2013:i:2:p:237-267

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10463/PS2

DOI: 10.1007/s10463-012-0371-z

Access Statistics for this article

Annals of the Institute of Statistical Mathematics is currently edited by Tomoyuki Higuchi

More articles in Annals of the Institute of Statistical Mathematics from Springer, The Institute of Statistical Mathematics
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().