Title: Hierarchical ANOVA and F-tests for functional data with an application to highway traffic data in Taiwan
Authors: Wei-Hsueh Huang - National Tsing-Hua University (Taiwan) [presenting]
Li-Shan Huang - National Tsing Hua University (Taiwan)
Abstract: Some new tests for the one-way ANOVA problem for functional data are proposed. Based on local polynomial regression, exact local and global ANOVA expressions are obtained, forming hierarchical ANOVA structures for estimating individual curves, a mean curve within a group of functions, and an overall mean curve for all groups of functions. A local test taking account of functional structure is first developed to examining differences of functions in a neighborhood of a point. Combining local ANOVA quantities, a test statistic is formed to testing global functional ANOVA. We show that both the local and global test statistics have asymptotic F-distributions, and enjoy the ``Wilks phenomenon''. Simulation studies are presented to compare the proposed global ANOVA test with some tests in the literature. A real data example on traffic flows of Taiwan highways before and after a major earthquake in 2016 illustrates the proposed tests.