A0454
Title: Basis expansions for functional snippets
Authors: Zhenhua Lin - University of California, Davis (United States)
Jane-Ling Wang - University of California Davis (United States)
Qixian Zhong - Xiamen University (China) [presenting]
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. Mean and covariance estimation is investigated 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. This challenge is tackled 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 numerical studies.
