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Statistica Sinica 31 (2021), 773-796

ROBUST INFERENCE IN VARYING-COEFFICIENT ADDITIVE MODELS
FOR LONGITUDINAL/FUNCTIONAL DATA

Lixia Hu1, Tao Huang2 and Jinhong You2

1Shanghai Lixin University of Accounting and Finance and 2Shanghai University of Finance and Economics

Abstract: 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.

Key words and phrases: B-spline, M-estimator, SCAD, tensor product, varying-coefficient additive model.

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