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.
Langthaler, P. B., Pini, A., Bathke, A. A. C., Interval-Wise Testing of Functional Data Defined on Two-dimensional Domains, in Michele La Rocc, M. L. R., Brunero Lise, B. L., Luigi Salmas, L. S. (ed.), Nonparametric Statistics, Springer, Cham 2020: 305- 313. 10.1007/978-3-030-57306-5_28 [http://hdl.handle.net/10807/167255]
Interval-Wise Testing of Functional Data Defined on Two-dimensional Domains
Pini, Alessia;
2020
Abstract
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.
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