Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Nonlinear models with measurement errors subject to single-indexed distortion

Language

English

Abstract

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. © 2012 Elsevier Inc.

Keywords

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

Publication Date

2012

Source Publication Title

Journal of Multivariate Analysis

Volume

112

Start Page

1

End Page

12

Publisher

Elsevier

DOI

10.1016/j.jmva.2012.05.012

Link to Publisher's Edition

http://dx.doi.org/10.1016/j.jmva.2012.05.012

ISSN (print)

0047259X

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