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 Use of Depth Measure for Multivariate Functional Data in Disease Prediction: An Application to Electrocardiograph Signals

2015 ◽  
Vol 11 (2) ◽  
Author(s):  
Nicholas Tarabelloni ◽  
Francesca Ieva ◽  
Rachele Biasi ◽  
Anna Maria Paganoni
Keyword(s):  
Functional Data ◽  
Simulation Studies ◽  
Bundle Branch Block ◽  
Ecg Signals ◽  
Covariance Operators ◽  
Multivariate Functional Data ◽  
Nonparametric Comparison ◽  
Two Populations ◽  
Generalized Regression Model

AbstractIn this paper we develop statistical methods to compare two independent samples of multivariate functional data that differ in terms of covariance operators. In particular we generalize the concept of depth measure to this kind of data, exploiting the role of the covariance operators in weighting the components that define the depth. Two simulation studies are carried out to validate the robustness of the proposed methods and to test their effectiveness in some settings of interest. We present an application to Electrocardiographic (ECG) signals aimed at comparing physiological subjects and patients affected by Left Bundle Branch Block. The proposed depth measures computed on data are then used to perform a nonparametric comparison test among these two populations. They are also introduced into a generalized regression model aimed at classifying the ECG signals.

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.

Gene trees: A powerful tool for exploring the evolutionary biology of species and speciation

2000 ◽  
Vol 15 (3) ◽  
pp. 211-222 ◽  
Author(s):  
Alan R. Templeton ◽  
Stephanie D. Maskas ◽  
Mitchell B. Cruzan
Keyword(s):  
Evolutionary Biology ◽  
Gene Trees
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