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Robust inference in varying-coefficient additive models for longitudinal/functional data. (English) Zbl 1469.62429

Summary: This study provides a robust inference for a varying-coefficient additive model for sparse or dense longitudinal/functional data. A spline-based three-step M-estimation method is proposed for estimating the varying-coefficient component functions and the additive component functions. In addition, the consistency and asymptotic normality of sparse data and dense data are investigated within a unified framework. Furthermore, employing a regularized M-estimation method, a model identification procedure is proposed that consistently identifies an additive term and a varying-coefficient term. Simulation studies are used to evaluate the finite-sample performance of the proposed methods, and confirm the asymptotic theory. Lastly, real-data examples demonstrate the applicability of the proposed methods.

MSC:

62R10 Functional data analysis
62G35 Nonparametric robustness
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References:

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[30] Lixia Hu School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai, China.
[31] Tao Huang School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai, China.
[32] Jinhong You School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai, China. E-mail: johnyou07@163.com (Received June 2018; accepted June 2019)
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