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Activity Number:
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89
- Nonparametric Methods for Modern Data
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Type:
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Contributed
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Date/Time:
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Monday, August 9, 2021 : 10:00 AM to 11:50 AM
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Sponsor:
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Section on Nonparametric Statistics
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Abstract #319165
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Title:
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Autoregressive Optimal Transport Models
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Author(s):
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Changbo Zhu* and Hans-Georg Müller
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Companies:
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University of California, Davis and University of California, Davis
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Keywords:
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Distributional Data Analysis;
Distributional Regression;
Distributional Time Series;
Iterated Random Function;
Optimal Transport;
Wasserstein space
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Abstract:
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Series of 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 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. In addition to simulations, the proposed models are illustrated with distributional time series of house prices across U.S. counties and of stock returns across the S&P 500 stock index.
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Authors who are presenting talks have a * after their name.
