### Partially Linear Single-Index Model in the Presence of Measurement Error

LIN Hongmei1,2, SHI Jianhong3, TONG Tiejun4, ZHANG Riquan5

1. 1. School of Statistics and Information, Shanghai University of International Business and Economics, Shanghai 201620, China;
2. Key Laboratory of Advanced Theory and Application in Statistics and Data Science, Ministry of Education, East China Normal University, Shanghai 200062, China;
3. School of Mathematics and Computer Science, Shanxi Normal University, Linfen 041081, China;
4. School of Mathematics and Computer Science, Shanxi Normal University, Linfen 041081, China;
5. School of Statistics, East China Normal University, Shanghai 200062, China
• Received:2021-04-12 Revised:2021-07-04 Online:2022-11-25 Published:2022-12-23
• Supported by:
This research was supported by the National Natural Science Foundation of China under Grant Nos. 11971171, 11971300, 11901286, 12071267 and 12171310, the Shanghai Natural Science Foundation under Grant No. 20ZR1421800, the Open Research Fund of Key Laboratory of Advanced Theory and Application in Statistics and Data Science (East China Normal University), the General Research Fund (HKBU12303421, HKBU12303918) and the Initiation Grant for Faculty Niche Research Areas (RC-FNRA-IG/20-21/SCI/03) of Hong Kong Baptist University.

LIN Hongmei, SHI Jianhong, TONG Tiejun, ZHANG Riquan. Partially Linear Single-Index Model in the Presence of Measurement Error[J]. Journal of Systems Science and Complexity, 2022, 35(6): 2361-2380.

The partially linear single-index model (PLSIM) is a flexible and powerful model for analyzing the relationship between the response and the multivariate covariates. This paper considers the PLSIM with measurement error possibly in all the variables. The authors propose a new efficient estimation procedure based on the local linear smoothing and the simulation-extrapolation method, and further establish the asymptotic normality of the proposed estimators for both the index parameter and nonparametric link function. The authors also carry out extensive Monte Carlo simulation studies to evaluate the finite sample performance of the new method, and apply it to analyze the osteoporosis prevention data.
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