报告题目：Robust Inference forVarying-coefficient Additive Model with Longitudinal/Functional Data
报 告 人：尤进红教授 (上海财经大学)
A varying-coefficient additive model (VCAM)has been applied to the analysis of functional data and locally stationary timeseries. In this paper, we focus on the robust inference of a VCAM with sparseor dense longitudinal/functional data. A spline-based three-step M-estimator isproposed to estimate the varying-coefficient component functions and additivecomponent functions, respectively. It is shown that the proposed estimators areconsistent and follow normal distributions asymptotically, which yields apointwise confidence interval (CI) of a univariate component function. Aboveall, the estimates possess oracle property in the sense that the iterationprocedure does not produce additional asymptotic errors, as if more informationon the component functions were known. For the purpose of model diagnosis, amodel identification procedure based on the regularized M-estimation method isproposed and is shown that it can consistently identify an additive term and avarying-coefficient term. Extensive Monte Carlo experiments investigating thefinite-sample performance of our estimation method and model identificationprocedure confirm the asymptotic theory. Real-life examples illustrating ourmethods are also considered.