@article{8d7c6fac165e4157af9db4d0e2cf212a,
title = "SIMEX estimation for single-index model with covariate measurement error",
abstract = "In this paper, we consider the single-index measurement error model with mismeasured covariates in the nonparametric part. To solve the problem, we develop a simulation-extrapolation (SIMEX) algorithm based on the local linear smoother and the estimating equation. For the proposed SIMEX estimation, it is not needed to assume the distribution of the unobserved covariate. We transform the boundary of a unit ball in Rp to the interior of a unit ball in Rp-1 by using the constraint ‖ β‖ = 1. The proposed SIMEX estimator of the index parameter is shown to be asymptotically normal under some regularity conditions. We also derive the asymptotic bias and variance of the estimator of the unknown link function. Finally, the performance of the proposed method is examined by simulation studies and is illustrated by a real data example.",
keywords = "Estimating equation, Local linear smoother, Measurement error, SIMEX, Single-index model",
author = "Yiping Yang and Tiejun Tong and Gaorong Li",
note = "Funding Information: Acknowledgements The authors would like to thank the Editor, the Associate Editor, and two reviewers for their insightful comments that led to a substantial improvement of an earlier manuscript. Gaorong Li{\textquoteright}s research was supported by the National Natural Science Foundation of China (11471029) and the Beijing Natural Science Foundation (1182003). Yiping Yang{\textquoteright}s research was supported by the National Natural Science Foundation of China (11301569), the Chongqing Research Program of Basic Theory and Advanced Technology (cstc2015jcyjA00023), Fifth batch of excellent talent support program for Chongqing Colleges and University and the Program for University Innovation Team of Chongqing (CXTDX201601026). Tiejun Tong{\textquoteright}s research was supported by the National Natural Science Foundation of China (11671338) and the Health and Medical Research Fund (04150476). Funding Information: The authors would like to thank the Editor, the Associate Editor, and two reviewers for their insightful comments that led to a substantial improvement of an earlier manuscript. Gaorong Li?s research was supported by the National Natural Science Foundation of China (11471029) and the Beijing Natural Science Foundation (1182003). Yiping Yang?s research was supported by the National Natural Science Foundation of China (11301569), the Chongqing Research Program of Basic Theory and Advanced Technology (cstc2015jcyjA00023), Fifth batch of excellent talent support program for Chongqing Colleges and University and the Program for University Innovation Team of Chongqing (CXTDX201601026). Tiejun Tong?s research was supported by the National Natural Science Foundation of China (11671338) and the Health and Medical Research Fund (04150476).",
year = "2019",
month = mar,
day = "1",
doi = "10.1007/s10182-018-0327-6",
language = "English",
volume = "103",
pages = "137--161",
journal = "AStA Advances in Statistical Analysis",
issn = "1863-8171",
publisher = "Springer Verlag",
number = "1",
}