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Activity Number: 485
Type: Topic Contributed
Date/Time: Wednesday, August 3, 2016 : 8:30 AM to 10:20 AM
Sponsor: Section on Statistical Learning and Data Science
Abstract #320776 View Presentation
Title: Nonparametric Estimation of Stationary Covariance Functions
Author(s): Li Wang* and Jiangyan Wang and Guanqun Cao
Companies: Iowa State University and Soochow University and Auburn University
Keywords: confidence band ; covariance function ; polynomial spline ; functionary data ; strong approximation

We consider nonparametric estimation and inference for stationary covariance functions of dense functional data. We propose an estimation procedure based on spline approximations of the mean function and the empirical covariance function. The proposed covariance estimator is smooth, consistent and asymptotically normal. We construct asymptotic simultaneous confidence bands for the true covariance. A constrained polynomial spline estimator is proposed to smooth the empirical covariance estimator. The proposed estimator is not only smooth but also positive definite. We conduct simulation experiments to evaluate the numerical performance of the proposed methods. The proposed method is also illustrated by a real data example.

Authors who are presenting talks have a * after their name.

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