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Linear manifold modelling of multivariate functional data
Author(s) -
Chiou JengMin,
Müller HansGeorg
Publication year - 2014
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/rssb.12038
Subject(s) - multivariate statistics , functional data analysis , multivariate analysis , linear model , component (thermodynamics) , set (abstract data type) , manifold (fluid mechanics) , data set , principal component analysis , mathematics , computer science , statistics , engineering , physics , mechanical engineering , thermodynamics , programming language
Summary Multivariate functional data are increasingly encountered in data analysis, whereas statistical models for such data are not well developed yet. Motivated by a case‐study where one aims to quantify the relationship between various longitudinally recorded behaviour intensities for Drosophila flies, we propose a functional linear manifold model. This model reflects the functional dependence between the components of multivariate random processes and is defined through data‐determined linear combinations of the multivariate component trajectories, which are characterized by a set of varying‐coefficient functions. The time varying linear relationships that govern the components of multivariate random functions yield insights about the underlying processes and also lead to noise‐reduced representations of the multivariate component trajectories. The functional linear manifold model proposed is put to the task for an analysis of longitudinally observed behavioural patterns of flying, feeding, walking and resting over the lifespan of Drosophila flies and is also investigated in simulations.