Transportation-based functional ANOVA and PCA for covariance operators
Electronic Journal of Statistics, ISSN: 1935-7524, Vol: 18, Issue: 1, Page: 1887-1916
2024
- 1Citations
- 1Mentions
Metric Options: Counts1 Year3 YearSelecting the 1-year or 3-year option will change the metrics count to percentiles, illustrating how an article or review compares to other articles or reviews within the selected time period in the same journal. Selecting the 1-year option compares the metrics against other articles/reviews that were also published in the same calendar year. Selecting the 3-year option compares the metrics against other articles/reviews that were also published in the same calendar year plus the two years prior.
Example: if you select the 1-year option for an article published in 2019 and a metric category shows 90%, that means that the article or review is performing better than 90% of the other articles/reviews published in that journal in 2019. If you select the 3-year option for the same article published in 2019 and the metric category shows 90%, that means that the article or review is performing better than 90% of the other articles/reviews published in that journal in 2019, 2018 and 2017.
Citation Benchmarking is provided by Scopus and SciVal and is different from the metrics context provided by PlumX Metrics.
Example: if you select the 1-year option for an article published in 2019 and a metric category shows 90%, that means that the article or review is performing better than 90% of the other articles/reviews published in that journal in 2019. If you select the 3-year option for the same article published in 2019 and the metric category shows 90%, that means that the article or review is performing better than 90% of the other articles/reviews published in that journal in 2019, 2018 and 2017.
Citation Benchmarking is provided by Scopus and SciVal and is different from the metrics context provided by PlumX Metrics.
Metrics Details
- Citations1
- Citation Indexes1
- Mentions1
- News Mentions1
- News1
Most Recent News
Reports Outline Technology Findings from Leiden University (Transportation-based Functional Anova and Pca for Covariance Operators)
2024 JUN 12 (NewsRx) -- By a News Reporter-Staff News Editor at Tech Daily News -- Fresh data on Technology are presented in a new
Article Description
We consider the problem of comparing several samples of stochastic processes with respect to their second-order structure, and describing the main modes of variation in this second order structure, if present. These tasks can be seen as an Analysis of Variance (ANOVA) and a Principal Component Analysis (PCA) of covariance operators, respectively. They arise naturally in functional data analysis, where several populations are to be contrasted relative to the nature of their dispersion around their means, rather than relative to their means themselves. We contribute a novel approach based on optimal (multi)transport, where each covariance can be identified with a a centred Gaussian process of corresponding covariance. By means of constructing the optimal simultaneous coupling of these Gaussian processes, we contrast the (linear) maps that achieve it with the identity with respect to a norm-induced distance. The resulting test statistic, calibrated by permutation, is seen to distinctly outperform the state-of-the-art, and to furnish considerable power even under local alternatives. This effect is seen to be genuinely functional, and is related to the potential for perfect discrimination in infinite dimensions. In the event of a rejection of the null hypothesis stipulating equality, a geometric interpretation of the transport maps allows us to construct a (tangent space) PCA revealing the main modes of variation. As a necessary step to developing our methodology, we prove results on the existence and boundedness of optimal multitransport maps. These are of independent interest in the theory of transport of Gaussian processes. The transportation ANOVA and PCA are illustrated on a variety of simulated and real examples.
Bibliographic Details
http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=85194186884&origin=inward; http://dx.doi.org/10.1214/24-ejs2240; https://projecteuclid.org/journals/electronic-journal-of-statistics/volume-18/issue-1/Transportation-based-functional-ANOVA-and-PCA-for-covariance-operators/10.1214/24-EJS2240.full; https://dx.doi.org/10.1214/24-ejs2240; https://projecteuclid.org/access-suspended
Institute of Mathematical Statistics
Provide Feedback
Have ideas for a new metric? Would you like to see something else here?Let us know