Abstract
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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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.
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Lin, H., Shi, J., Tong, T. et al. Partially Linear Single-Index Model in the Presence of Measurement Error. J Syst Sci Complex 35, 2361–2380 (2022). https://doi.org/10.1007/s11424-022-1112-x
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DOI: https://doi.org/10.1007/s11424-022-1112-x