Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Latent Transport Models for Multivariate Functional Data   Multivariate functional data present theoretical and practical complications
which are not found in univariate functional data. One of these is a situation
where the component functions of multivariate functional data are positive and
are subject to mutual time warping. That is, the component processes exhibit a
similar shape but are subject to systematic phase variation across their time
domains. We introduce a novel model for multivariate functional data that
incorporates such mutual time warping via nonlinear transport functions. This
model allows for meaningful interpretation and is well suited to represent
functional vector data. The proposed approach combines a random amplitude
factor for each component with population based registration across the
components of a multivariate functional data vector and also includes a latent
population function, which corresponds to a common underlying trajectory as
well as subject-specific warping component. We also propose estimators for all
components of the model. The proposed approach not only leads to a novel
representation for multivariate functional data, but is also useful for
downstream analyses such as Fr\'echet regression. Rates of convergence are
established when curves are fully observed or observed with measurement error.
The usefulness of the model, interpretations and practical aspects are
illustrated in simulations and with application to multivariate human growth
curves as well as multivariate environmental pollution data.

31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ