Fréchet Covariance and MANOVA Tests for Random Objects in Multiple Metric Spaces

2023/06/21 by Alex Fout, Bailey K. Fosdick, Fout, Alex +1 · 1 citation
Computer Science · Environmental Science · Mathematics · #Advanced Statistical Methods and Models #Data Management and Algorithms #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Soil Geostatistics and Mapping #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2306.12066

openalex publication_date 2023/06/21 · openalex created_date 2023/06/24 · openalex updated_date 2026/07/28

Abstract

In this manuscript we consider random objects being measured in multiple metric spaces, which may arise when those objects may be measured in multiple distinct ways. In this new multivariate setting, we define a Fréchet covariance and Fréchet correlation in two metric spaces, and a Fréchet covariance matrix and Fréchet correlation matrix in an arbitrary number of metric spaces. We prove consistency for the sample Fréchet covariance, and propose several tests to compare the means and covariance matrices between two or more groups. Lastly, we investigate the power and Type I error of each test under a variety of scenarios.

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