An approach to Canonical Correlation Analysis based on Rényi's Pseudodistances

M. Jaenada Malagón, P. Miranda Menéndez, L. Pardo, K. Zografos

Se presenta un nuevo método para detectar relaciones lineales entre dos vectores aleatorios a partir de las pseudodistancias de Renyi. El objetivo es encontrar combinaciones lineales de las componentes de cada vector que estén muy relacionadas. Al contrario que el Análisis de Correlación Canónica clásico, este nuevo procedimiento es capaz de detectar también relaciones no lineales. Este método recoge como caso particular el método ICCA de Yin, pero lo mejora en el sentido de que es robusto frente a datos contaminados, i.e. outliers. Se estudian varias propiedades teóricas de este procedimiento y su aplicación en el caso práctico donde las distribuciones son desconocidas. Para este último caso se presenta un estimador consistente. Se estudia también el número adecuado de combinaciones lineales que recogen todas las relaciones entre los vectores aleatorios. Finalmente, se presenta un estudio de simulación para ver el comportamiento de este método y compararlo con otros métodos.

Keywords: Information Canonical Correlation Analysis, Renyi's pseudodistances, robustness

Scheduled

GT04 Multivariate Analysis and Classification III
June 7, 2022  4:50 PM
Cloister room

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