Nonparametric Estimation of Stationary Covariance Functions

• 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
• 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

Abstract

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.