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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| Vydané v: | Advances in data analysis and classification Ročník 18; číslo 2; s. 431 - 454 |
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| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
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Berlin/Heidelberg
Springer Berlin Heidelberg
01.06.2024
Springer Nature B.V |
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| ISSN: | 1862-5347, 1862-5355 |
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| Abstract | 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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| AbstractList | 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. |
| Author | Smaga, Łukasz Krzyśko, Mirosław |
| Author_xml | – sequence: 1 givenname: Mirosław surname: Krzyśko fullname: Krzyśko, Mirosław organization: Interfaculty Institute of Mathematics and Statistics, Calisia University-Kalisz – sequence: 2 givenname: Łukasz orcidid: 0000-0002-2442-8816 surname: Smaga fullname: Smaga, Łukasz email: ls@amu.edu.pl organization: Faculty of Mathematics and Computer Science, Adam Mickiewicz University |
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| Cites_doi | 10.1007/978-0-387-98185-7 10.1016/j.csda.2018.02.002 10.1080/00401706.2016.1156024 10.1016/j.spl.2014.11.012 10.1146/annurev-statistics-041715-033624 10.1093/biostatistics/kxu006 10.1093/biomet/ass037 10.1214/14-AOS1255 10.1093/biomet/asz024 10.1007/s11634-013-0162-2 10.1214/aoms/1177697287 10.1007/s10260-020-00548-0 10.1080/00273171.2019.1627513 10.1007/978-1-4614-3655-3 10.1021/ct300565f 10.1016/j.jspi.2013.04.002 10.1080/02331888.2014.896917 10.1073/pnas.1217269109 10.1007/s11634-013-0158-y 10.1080/01621459.2012.695654 10.1214/17-AOS1579 10.1214/19-AOS1935 10.1111/sjos.12025 10.1214/12-AOP803 10.1214/009053607000000505 10.1214/19-AOS1934 10.18637/jss.v051.i04 10.1093/biomet/asx043 10.1080/01621459.2018.1483827 10.1007/s00180-018-0842-7 10.1016/j.jmva.2013.02.012 10.5281/zenodo.3468124 10.1007/b98886 10.32614/CRAN.package.dcortools 10.1007/978-1-4614-1412-4_45 10.1007/b98888 10.1201/b15005 10.1007/978-3-540-78534-7_8 10.1007/11564089_7 |
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| Keywords | Variability measure 62H15 62R10 Distance correlation Projection correlation Standard deviation Functional data analysis |
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| SubjectTerms | 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 |
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| Title | Application of distance standard deviation in functional data analysis |
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