scholarly journals Permutation tests for equality of distributions of functional data

2018 ◽  
Author(s):  
Federico A. Bugni ◽  
Joel L. Horowitz
Keyword(s):  
Functional Data ◽  
Permutation Tests

scholarly journals Permutation tests for the equality of covariance operators of functional data with applications to evolutionary biology

2017 ◽  
Vol 11 (2) ◽  
pp. 3815-3840 ◽  
Author(s):  
Alessandra Cabassi ◽  
Davide Pigoli ◽  
Piercesare Secchi ◽  
Patrick A. Carter
Keyword(s):  
Functional Data ◽  
Evolutionary Biology ◽  
Permutation Tests ◽  
Covariance Operators

scholarly journals Functional Symmetry and Statistical Depth for the Analysis of Movement Patterns in Alzheimer’s Patients

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 820
Author(s):  
Alicia Nieto-Reyes ◽  
Heather Battey ◽  
Giacomo Francisci
Keyword(s):  
Functional Data Analysis ◽  
Functional Data ◽  
Permutation Tests ◽  
Movement Patterns ◽  
Movement Pattern ◽  
Black Box ◽  
Underlying Distribution ◽  
Statistical Depth ◽  
The Difference ◽  
Functional Symmetry

Black-box techniques have been applied with outstanding results to classify, in a supervised manner, the movement patterns of Alzheimer’s patients according to their stage of the disease. However, these techniques do not provide information on the difference of the patterns among the stages. We make use of functional data analysis to provide insight on the nature of these differences. In particular, we calculate the center of symmetry of the underlying distribution at each stage and use it to compute the functional depth of the movements of each patient. This results in an ordering of the data to which we apply nonparametric permutation tests to check on the differences in the distribution, median and deviance from the median. We consistently obtain that the movement pattern at each stage is significantly different to that of the prior and posterior stage in terms of the deviance from the median applied to the depth. The approach is validated by simulation.

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