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Autoregressive optimal transport models
Series of univariate distributions indexed by equally spaced time points are ubiquitous in applications and their analysis constitutes one of the challenges of the emerging field of distributional data analysis. To quantify such distributional time series, we propose a class of intrinsic autoregress...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Oxford University Press
2023
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10376456/ https://www.ncbi.nlm.nih.gov/pubmed/37521164 http://dx.doi.org/10.1093/jrsssb/qkad051 |
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author | Zhu, Changbo Müller, Hans-Georg |
author_facet | Zhu, Changbo Müller, Hans-Georg |
author_sort | Zhu, Changbo |
collection | PubMed |
description | Series of univariate distributions indexed by equally spaced time points are ubiquitous in applications and their analysis constitutes one of the challenges of the emerging field of distributional data analysis. To quantify such distributional time series, we propose a class of intrinsic autoregressive models that operate in the space of optimal transport maps. The autoregressive transport models that we introduce here are based on regressing optimal transport maps on each other, where predictors can be transport maps from an overall barycenter to a current distribution or transport maps between past consecutive distributions of the distributional time series. Autoregressive transport models and their associated distributional regression models specify the link between predictor and response transport maps by moving along geodesics in Wasserstein space. These models emerge as natural extensions of the classical autoregressive models in Euclidean space. Unique stationary solutions of autoregressive transport models are shown to exist under a geometric moment contraction condition of Wu & Shao [(2004) Limit theorems for iterated random functions. Journal of Applied Probability 41, 425–436)], using properties of iterated random functions. We also discuss an extension to a varying coefficient model for first-order autoregressive transport models. In addition to simulations, the proposed models are illustrated with distributional time series of house prices across U.S. counties and annual summer temperature distributions. |
format | Online Article Text |
id | pubmed-10376456 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2023 |
publisher | Oxford University Press |
record_format | MEDLINE/PubMed |
spelling | pubmed-103764562023-07-29 Autoregressive optimal transport models Zhu, Changbo Müller, Hans-Georg J R Stat Soc Series B Stat Methodol Original Article Series of univariate distributions indexed by equally spaced time points are ubiquitous in applications and their analysis constitutes one of the challenges of the emerging field of distributional data analysis. To quantify such distributional time series, we propose a class of intrinsic autoregressive models that operate in the space of optimal transport maps. The autoregressive transport models that we introduce here are based on regressing optimal transport maps on each other, where predictors can be transport maps from an overall barycenter to a current distribution or transport maps between past consecutive distributions of the distributional time series. Autoregressive transport models and their associated distributional regression models specify the link between predictor and response transport maps by moving along geodesics in Wasserstein space. These models emerge as natural extensions of the classical autoregressive models in Euclidean space. Unique stationary solutions of autoregressive transport models are shown to exist under a geometric moment contraction condition of Wu & Shao [(2004) Limit theorems for iterated random functions. Journal of Applied Probability 41, 425–436)], using properties of iterated random functions. We also discuss an extension to a varying coefficient model for first-order autoregressive transport models. In addition to simulations, the proposed models are illustrated with distributional time series of house prices across U.S. counties and annual summer temperature distributions. Oxford University Press 2023-05-12 /pmc/articles/PMC10376456/ /pubmed/37521164 http://dx.doi.org/10.1093/jrsssb/qkad051 Text en © The Royal Statistical Society 2023. https://creativecommons.org/licenses/by-nc/4.0/This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial License (https://creativecommons.org/licenses/by-nc/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact journals.permissions@oup.com |
spellingShingle | Original Article Zhu, Changbo Müller, Hans-Georg Autoregressive optimal transport models |
title | Autoregressive optimal transport models |
title_full | Autoregressive optimal transport models |
title_fullStr | Autoregressive optimal transport models |
title_full_unstemmed | Autoregressive optimal transport models |
title_short | Autoregressive optimal transport models |
title_sort | autoregressive optimal transport models |
topic | Original Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10376456/ https://www.ncbi.nlm.nih.gov/pubmed/37521164 http://dx.doi.org/10.1093/jrsssb/qkad051 |
work_keys_str_mv | AT zhuchangbo autoregressiveoptimaltransportmodels AT mullerhansgeorg autoregressiveoptimaltransportmodels |