Empirical Likelihood Methods on Functional Time Series Data

• Activity Number: 520 - Contributed Poster Presentations: Business and Economic Statistics Section
• Type: Contributed
• Date/Time: Wednesday, August 2, 2017 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Guangxing Wang* and Wolfgang Polonik
• Companies: University of California, Davis and University of California, Davis
• Keywords: Empirical Likelihood ; Functional Time Series ; Empirical Likelihood Ratio ; Weakly Dependent Functional data ; Functional Principal Component Analysis ; Empirical Likelihood Confidence Region

Abstract

Empirical likelihood (EL) methods play an important role in statistical inference. They combine the reliability of nonparametric methods with the effectiveness and flexibility of likelihood methods. Though there are extensive studies for finite dimensional settings, the study of EL methods on functional data is scarce. This is particularly true for dependent functional data. In this presentation, we indicate how to apply EL methods to linear functional time series data by considering a functional AR(1) model. First, we introduce an empirical maximum likelihood estimator of the kernel operator, and show its asymptotic consistency and normality. Then, we demonstrate how to utilize the asymptotic distribution of the empirical likelihood ratio to construct a confidence region for the operator.