%0 Journal Article
%A Jaenada Malagón, María
%A Miranda Menéndez, Pedro
%A Pardo Llorente, Leandro
%A Zografos, Konstantinos
%T An Approach to Canonical Correlation Analysis Based on Rényi’s Pseudodistances
%D 2023
%@ 1099-4300
%U https://hdl.handle.net/20.500.14352/87289
%X 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.
%~