Permutation MANOVA for Functional Linear Models and Regionalized Follow-Up Tests

• Activity Number: 338
• Type: Topic Contributed
• Date/Time: Tuesday, August 3, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Mark C. Greenwood*+
• Companies: Montana State University
• Keywords: Permutation tests ; Functional Data Analysis ; Functional ANOVA ; Distance-based methods ; perMANOVA

Abstract

Functional ANOVA (FANOVA) involves a functional response for each observation from k groups, with an interest in testing for a difference in the functional means between the groups. A functional F-statistic that parallels the standard F-statistic and is a continuous function of time is the basis of many FANOVA test statistics. Recommendations for either tracking the maximum or integral of this statistic have been made for performing an overall test in FANOVA. The equivalence between the integrated F-statistic and a distance-based approach is shown, connecting the statistics used in a variety of related papers to a general class of distance-based testing methods called permutation MANOVA. A method for generating regionalized follow-up tests is also developed. An application of the methods to testing for differences in the shape of valley elevation cross-profiles is presented.