Department of Mathematics
Nonlinear models with measurement errors subject to single-indexed distortion
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.
Covariate-adjusted regression, Distorting function, Empirical likelihood, Error-prone, Estimating equation function, Local linear smoothing, Measurement errors models, Single index
Source Publication Title
Journal of Multivariate Analysis
Zhang, Jun, Li-Xing Zhu, and Hua Liang. "Nonlinear models with measurement errors subject to single-indexed distortion." Journal of Multivariate Analysis 112 (2012): 1-12.