High-Dimensional Empirical Likelihood Methods for Dependent Functional Data

• Activity Number: 303 - Statistical Association and High-Dimensional Data
• Type: Contributed
• Date/Time: Tuesday, July 30, 2019 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Guangxing Wang* and Wolfgang Polonik
• Companies: University of California, Davis and University of California, Davis
• Keywords: High dimensional empirical likelihood; Dependent functional data; High dimensional inference; Coverage accuracy; Penalized empirical likelihood; EL confidence region

Abstract

With the availability of modern and complex data, functional data analysis techniques become increasingly important and indispensable in many applications. Here we discuss an empirical likelihood method for constructing an estimator for a functional parameter of interest based on dependent functional data. Our method using basis expansions and along with a penalization approach, allows the number of basis functions to grow as sample size increases. This enables us to obtain a maximum empirical likelihood estimator that converges to the fully functional true parameter of interest. Moreover, we show that our method breaks free from the convex hull constraint; therefore, it provides an empirical likelihood confidence region with improved coverage accuracy. Automatic tuning parameter selection is also discussed.