Application of distance standard deviation in functional data analysis

This paper concerns the measurement and testing of equality of variability of functional data. We apply the distance standard deviation constructed based on distance correlation, which was recently introduced as a measure of spread. For functional data, the distance standard deviation seems to measu...

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Bibliographic Details
Published in:Advances in data analysis and classification Vol. 18; no. 2; pp. 431 - 454
Main Authors: Krzyśko, Mirosław, Smaga, Łukasz
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2024
Springer Nature B.V
Subjects:
Chemistry and Earth Sciences
Computer Science
Data analysis
Data Mining and Knowledge Discovery
Economics
Equality
Finance
Health Sciences
Humanities
Hypotheses
Hypothesis testing
Insurance
Investigations
Law
Management
Mathematics and Statistics
Medicine
Original Article
Permutations
Physics
Quality control
Random variables
Real numbers
Simulation
Standard deviation
Statistical inference
Statistical Theory and Methods
Statistics
Statistics for Business
Statistics for Engineering
Statistics for Life Sciences
Statistics for Social Sciences
Time series
Variability measure
62H15
62R10
Distance correlation
Projection correlation
Standard deviation
Functional data analysis
ISSN:1862-5347, 1862-5355
Online Access:Get full text
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Summary:This paper concerns the measurement and testing of equality of variability of functional data. We apply the distance standard deviation constructed based on distance correlation, which was recently introduced as a measure of spread. For functional data, the distance standard deviation seems to measure different kinds of variability, not only scale differences. Moreover, the distance standard deviation is just one real number, and for this reason, it is of more practical value than the covariance function, which is a more difficult object to interpret. For testing equality of variability in two groups, we propose a permutation method based on centered observations, which controls the type I error level much better than the standard permutation method. We also consider the applicability of other correlations to measure the variability of functional data. The finite sample properties of two-sample tests are investigated in extensive simulation studies. We also illustrate their use in five real data examples based on various data sets.
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ISSN:1862-5347
1862-5355
DOI:10.1007/s11634-023-00538-6