| dbo:abstract |
In statistics and in probability theory, distance correlation or distance covariance is a measure of dependence between two paired random vectors of arbitrary, not necessarily equal, dimension. The population distance correlation coefficient is zero if and only if the random vectors are independent. Thus, distance correlation measures both linear and nonlinear association between two random variables or random vectors. This is in contrast to Pearson's correlation, which can only detect linear association between two random variables. Distance correlation can be used to perform a statistical test of dependence with a permutation test. One first computes the distance correlation (involving the re-centering of Euclidean distance matrices) between two random vectors, and then compares this value to the distance correlations of many shuffles of the data. (en) En estadística y en teoría de la probabilidad, la correlación de la distancia o covarianza de la distancia es una medida de dependencia entre dos vectores aleatorios emparejados, de dimensión arbitraria y no necesariamente igual. El coeficiente de correlación de la distancia poblacional es cero si y solo si los vectores aleatorios son independientes. Por lo tanto, la correlación de la distancia mide tanto la asociación lineal como la no lineal entre dos variables aleatorias o vectores aleatorios. Esto contrasta con el coeficiente de correlación de Pearson, que solo puede detectar una asociación lineal entre dos variables aleatorias. La correlación de la distancia se puede utilizar para realizar una prueba estadística de dependencia con un remuestreo. En un primer paso se calcula la correlación de la distancia (que implica el recentrado de las matrices de la distancia euclidianas) entre dos vectores aleatorios, y luego se compara este valor con las correlaciones de la distancia de muchos cruces de datos. (es) |
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http://projecteuclid.org/download/pdfview_1/euclid.aoas/1267453933 http://projecteuclid.org/download/pdfview_1/euclid.aoas/1267453934 http://personal.bgsu.edu/~mrizzo/energy.htm https://zenodo.org/record/1431597 https://cran.r-project.org/web/packages/energy/index.html |
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| rdfs:comment |
In statistics and in probability theory, distance correlation or distance covariance is a measure of dependence between two paired random vectors of arbitrary, not necessarily equal, dimension. The population distance correlation coefficient is zero if and only if the random vectors are independent. Thus, distance correlation measures both linear and nonlinear association between two random variables or random vectors. This is in contrast to Pearson's correlation, which can only detect linear association between two random variables. (en) En estadística y en teoría de la probabilidad, la correlación de la distancia o covarianza de la distancia es una medida de dependencia entre dos vectores aleatorios emparejados, de dimensión arbitraria y no necesariamente igual. El coeficiente de correlación de la distancia poblacional es cero si y solo si los vectores aleatorios son independientes. Por lo tanto, la correlación de la distancia mide tanto la asociación lineal como la no lineal entre dos variables aleatorias o vectores aleatorios. Esto contrasta con el coeficiente de correlación de Pearson, que solo puede detectar una asociación lineal entre dos variables aleatorias. (es) |
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Correlación de la distancia (es) Distance correlation (en) |
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