Nonlinear models with measurement errors subject to single-indexed distortion

Jun Zhang, Li-Xing Zhu and Hua Liang

Journal of Multivariate Analysis, 2012, vol. 112, issue C, 1-23

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.

Keywords: Covariate-adjusted regression; Error-prone; Empirical likelihood; Estimating equation function; Local linear smoothing; Measurement errors models; Single index; Distorting function (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (6)

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DOI: 10.1016/j.jmva.2012.05.012

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