American Statistical Association
New York City
Metropolitan Area Chapter

Levin Lecture Series: Fall 2019 Colloquium Seminars
Department of Biostatistics
Mailman School of Public Health
Columbia University



HIERARCHICAL TESTS FOR FUNCTIONAL DATA
WITH AN APPLICATION TO TRAFFIC FLOWS

by

Dr. Li-Shan Huang
Professor, Institute of Statistics
National Tsing Hua University

Host: Zhezhen Jin


Abstract

In this paper, some new tests for functional data are proposed. For multiple-sample functional ANOVA (fANOVA), based on local polynomial regression, a hierarchical structure for estimating individual curves, a mean curve within a group of functions, and an overall mean curve for all groups of functions is formed, and exact local and global ANOVA decompositions are obtained. A local fANOVA test is developed to examine differences between groups of curves in a local neighborhood. Combining local ANOVA quantities, a test statistic is formed to testing global fANOVA. We show that both the local and global fANOVA test statistics have asymptotic F-distributions, are location and scale invariant, and enjoy the Wilks phenomenon. In addition, the proposed fANOVA tests have an invariant property that allows interchanging the order of smoothing and ANOVA projection, while existing works in the literature mostly focus on the approach of smoothing first and then performing fANOVA. The investigations are extended to one-sample tests examining whether a group of curves share a common mean curve. Simulation studies are presented to compare the proposed global fANOVA 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.

This is joint work with a student Wei-Hsueh Huang.


Date: Monday, November 25, 2019
Time: 11:30 A.M. - 12:30 P.M.
Location: Mailman School of Public Health
Department of Biostatistics
722 West 168th Street
AR Building
6th Floor, Room 657
New York, New York

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