B0901
Title: Testing equality of covariance operators/matrices for functional/high-dimensional data
Authors: Jin Yang - The Hong Kong polytechnic University (Hong Kong)
Tao Zhang - Guangxi University of Science and Technology (China)
Catherine Liu - The Hong Kong Polytechnic University (Hong Kong) [presenting]
Abstract: The purpose is twofold. The first goal is to propose a unified methodology for testing equality of covariance operators of two functional samples whatever the type of the functional data is dense or sparse, balanced or irregularly spaced. A two-step procedure is developed which leads to a global testing statistic. The second goal is, from the insight of functional data analysis, to present a novel method to test equality of covariance matrices of two high-dimensional samples. It might be an inchoate but inspiring trying to apply the idea of functional data analysis into high-dimensional data study. Under null and alternative hypotheses, asymptotic distributions of the testing statistics have been derived for afore two types of data. Extensive simulation experiments have been conducted demonstrating consistency of the tests for both data scenarios. In finite sample numerical analysis, the proposed approaches outperform existing work in terms of both size and power for equality testing problems for both functional data and high-dimensional data. Two applications are provided: Air pollution data in Southwestern area of China is analyzed to illustrate our procedure of testing equality of covariance operators for functional data samples; Mitochondrial calcium concentration data is analyzed to demonstrate how our proposed method can be applied to test equality of covariance matrices for high-dimensional data.
