Interval-Wise Testing of Functional Data Defined on Two-dimensional Domains

Functional Data Analysis is the statistical analysis of data sets composed of functions of a continuous variable on a given domain. Previous work in this area focuses on one-dimensional domains. In this work, we extend a method developed for the one-dimensional case, the interval-wise testing procedure (IWT), to the case of a two-dimensional domain. We first briefly explain the theory of the IWT for the one-dimensional case, followed by a proposed extension to the two-dimensional case. We also discuss challenges that appear in the two-dimensional case but do not exist in the one-dimensional case. Finally, we provide results of a simulation study to explore the properties of the new procedure in more detail.