Leiden University Student Repository

Hackmann, Toby (2023)

Comparing test statistics of two-sample permutation tests based on covariance of functional data

Master thesis | Statistics and Data Science (MSc)

With modern measurement techniques, the prominence of data that can be best described as functional data is increasing. Statistical techniques for comparing the means of two samples of functional data are well studied, but less is known about tests for comparisons of covariance. We compare several methods to estimate the covariance and multiple test statistics in a power analysis of a dataset, and a simulation study. Our results show that, in a two-sample permutation test of the phoneme data set from the fda package in R, some of the test statistics seem to have a power of 1.000, while others show more reasonable power levels in the 0.500-0.700 range. A simulation study shows that the power of a two-sample permutation test can differ vastly between test statistics, depending on the type difference between the covariances of the two samples. This means that a test statistic must be chosen very carefully by researchers.

fda, functional data analysis, covariance, second order analysis, simulation

Author

Hackmann, Toby

Faculty

Faculty of Science

Supervisors

Masarotto, V.

ECTS Credits

34

Evaluation

Recommended

Language

en