Jaenada Malagón, MaríaMiranda Menéndez, PedroPardo Llorente, LeandroZografos, Konstantinos2023-07-202023-07-202023-04-251099-430010.3390/e25050713https://hdl.handle.net/20.500.14352/87289Canonical 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.engAttribution 4.0 Internationaljournal articlehttps://www.mdpi.com/1099-4300/25/5/713open access519.237Information canonical correlation analysisKullback-Leibler divergenceMutual informationRenyi's pseudodistancesRobustnessConsistencyEstadística matemática (Matemáticas)1209.09 Análisis Multivariante