Basis Expansions for Functional Snippets

• Activity Number: 10 - Advances in Functional and Geometric Data Analysis
• Type: Invited
• Date/Time: Sunday, August 8, 2021 : 1:30 PM to 3:20 PM
• Sponsor: IMS
• Author(s): Zhenhua Lin and Jane-Ling Wang* and Qixian Zhong
• Companies: National University of Singapore and UC Davis and Tsing Hua University
• Keywords: Covariance estimation; Fourier basis; Functional fragments; Longitudinal data; Penalization estimation

Abstract

Estimation of mean and covariance functions is fundamental for functional data analysis. While this topic has been studied extensively in the literature, a key assumption is that there are enough data in the domain of interest to estimate both the mean and covariance functions. In this paper, we investigate mean and covariance estimation for functional snippets in which observations from a subject are available only in an interval of length strictly (and often much) shorter than the length of the whole interval of interest. For such a sampling plan, no data is available for direct estimation of the off-diagonal region of the covariance function. We tackle this challenge via a basis representation of the covariance function. The proposed estimator enjoys a convergence rate that is adaptive to the smoothness of the underlying covariance function, and has superior finite-sample performance in simulation studies.