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Canonical Correlation Analysis (CCA) infers a pairwise linear relationship between two groups of random variables, X and Y. In this paper, we present a new procedure based on Rényi's pseudodistances (RP) aiming to detect linear and non-linear relationships between the two groups. RP canonical analysis (RPCCA) finds canonical coefficient vectors, a and b, by maximizing an RP-based measure. This new family includes the Information Canonical Correlation Analysis (ICCA) as a particular case and extends the method for distances inherently robust against outliers. We provide estimating techniques for RPCCA and show the consistency of the proposed estimated canonical vectors. Further, a permutation test for determining the number of significant pairs of canonical variables is described. The robustness properties of the RPCCA are examined theoretically and empirically through a simulation study, concluding that the RPCCA presents a competitive alternative to ICCA with an added advantage in terms of robustness against outliers and data contamination.
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| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC10217722 | PMC |
| http://dx.doi.org/10.3390/e25050713 | DOI Listing |
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