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Activity Number:
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486
- Advances in Spatial and Spatio-Temporal Statistics
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Type:
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Contributed
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Date/Time:
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Wednesday, August 10, 2022 : 2:00 PM to 3:50 PM
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Sponsor:
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Section on Statistics and the Environment
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Abstract #323151
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Title:
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A Multivariate Criterion for Spatial Aggregation
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Author(s):
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Ranadeep Daw* and Christopher K. Wikle and Jonathan R Bradley and Scott H. Holan and Matthew Simpson
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Companies:
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University of Missouri and University of Missouri and Florida State University and University of Missouri/U.S. Census Bureau and SAS Institute
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Keywords:
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Spatiotemporal Statistics;
Basis Expansion;
Karhunen-Loeve Expansion;
Covariance Matrix;
Multivariate Stochastic Processes;
Change of Support Problem
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Abstract:
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The change of support (COS) problem in statistics demonstrates that the interpretation of spatial (or spatiotemporal) data analysis are affected by the choice of resolutions or territorial units used in the study. The ecological fallacy is one famous example of this phenomenon. In this talk, we investigate the COS problem for multivariate data with the goal of providing a data-driven discretization criterion for the domain of interest based on the aggregation errors. The discretization is based on a novel metric, called the Multivariate Criterion for Aggregation Error (MCAGE). Such multi-scale representations of an underlying (multivariate) process are often formulated in terms of basis expansions. We show that a particularly useful basis expansion in this context is based on the multivariate Karhunen-Loeve expansion, which satisfies the bi-orthogonality property by using orthonormal eigenfunctions and uncorrelated expansion coefficients. The MKLE bases are used as input features to construct the MCAGE, which then is minimized to get an optimal multivariate areal representation. The effectiveness of the approach is demonstrated through simulation and real data examples.
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Authors who are presenting talks have a * after their name.
