An Approach to Canonical Correlation Analysis Based on Rényi’s Pseudodistances
Canonical Correlation Analysis (CCA) infers a pairwise linear relationship between two groups of random variables, and . 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...
| Autores: | , , , |
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| Formato: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Recursos: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/87289 |
| Acesso em linha: | https://hdl.handle.net/20.500.14352/87289 |
| Access Level: | acceso abierto |
| Palavra-chave: | 519.237 Information canonical correlation analysis Kullback-Leibler divergence Mutual information Renyi's pseudodistances Robustness Consistency Estadística matemática (Matemáticas) 1209.09 Análisis Multivariante |
| Resumo: | Canonical Correlation Analysis (CCA) infers a pairwise linear relationship between two groups of random variables, and . 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, and , 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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