V. Pawlowsky-Glahn, J. J. Egozcue Rubí

Una composición es una clase de equivalencia de vectores con componentes proporcionales representada por un vector de D partes situado en un símplex. Sus componentes estrictamente positivas contienen información relativa. El espacio muestral de las composiciones de D partes es un símplex de dimensión D-1 dotado de estructura de espacio Euclídeo real, estructura que se conoce como geometría de Aitchison. Dada una muestra de tamaño N, la traspuesta de la matriz de datos conservará idénticas propiedades a la matriz original, hecho que permite estructurar el espacio de las partes como espacio Euclídeo real con la geometría de Aitchison. Por analogía con el espacio real, estudiamos las propiedades de relación entre partes y su dependencia de la subcomposición considerada. El resultado es que las medidas tradicionales de covarianza y correlación dependen de la subcomposición y son incoherentes, mientras que la distancia de Aitchison entre partes no depende de la subcomposición observada.

Keywords: datos composicionales, espacio de partes, geometría de Aitchison, correlación espuria

Scheduled

Multivariate Analysis I
June 8, 2022  4:00 PM
Cloister room


Other papers in the same session

Efficient imputation of unobserved values in high-throughput compositional data through singular value decomposition

J. Palarea-Albaladejo, J. A. Martín-Fernández, A. Ruiz-Gazen, C. Thomas-Agnan

Estimadores de mínima pseudodistancia de Rényi para modelos de regresión logística

J. M. Alonso Revenga, A. Calviño Martínez, S. Muñoz López

RadarTSR: Robust Adaptation for Datasets with Anomalous Rows and cells of Trimmed Scores Regression

A. González Cebrián, A. Folch Fortuny, F. J. Arteaga Moreno, A. J. Ferrer Riquelme


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