2009
DOI: 10.1214/09-aoas312
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Brownian distance covariance

Abstract: We discuss briefly the very interesting concept of Brownian distance covariance developed by Székely and Rizzo (2009) and describe two possible extensions. The first extension is for high dimensional data that can be coerced into a Hilbert space, including certain high throughput screening and functional data settings. The second extension involves very simple modifications that may yield increased power in some settings. We commend Székely and Rizzo for their very interesting work and recognize that this gene… Show more

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Cited by 670 publications
(602 citation statements)
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“…A pair of landmark papers (2,3) proposed the distance correlation as a measurement of multivariate independence, and others have recently built upon it (4-7). The method is extremely general in that it is applicable to random vectors of arbitrary and not necessarily equal dimension and only involves Euclidean pairwise distance.…”
mentioning
confidence: 99%
“…A pair of landmark papers (2,3) proposed the distance correlation as a measurement of multivariate independence, and others have recently built upon it (4-7). The method is extremely general in that it is applicable to random vectors of arbitrary and not necessarily equal dimension and only involves Euclidean pairwise distance.…”
mentioning
confidence: 99%
“…The first four are based on Pearson correlation, Kendall's rank correlation, the distance correlation (Székely et al, 2007) and the rank-based distance correlation (Székely and Rizzo, 2009), respectively. The distance correlation and rank-based distance correlation are also nonnegative with equality to zero if and only if two random variables are independent.…”
Section: An Estimationmentioning
confidence: 99%
“…In this section, we conduct some additional Monte Carlo simulations to evaluate the finite sample performance of our proposed MBKR-SIS method in comparison to five existing screening methods such as the SIS (Fan and Lv, 2008), SIRS (Zhu et al, 2011), Kendall's rank correlation based sure independent screening procedure , RRCS for short), distance correlation based on SIS (Li, Zhong and Zhu, 2012, DC-SIS for short) and the sure independent screening procedure using rank-based distance correlation (Székely and Rizzo, 2009, RDC-SIS for short).…”
Section: Some Additional Simulationsmentioning
confidence: 99%
“…Zhang et al [39] studied the world international shipping market, especially on evolutionary rules of MSTs, systemic risk, and the transmission relationship of Granger causality dynamics in pre-crisis and post-crisis times. Additionally, they replaced the Pearson distance of the traditional similarity index of sequences with Brownian distance, proposed by Székely and Rizzo [40], and better revealed the non-linear correlation among time series. Yao et al [41] characterized the correlation evolution of South China industrial electricity consumption in pre-crisis and post-crisis periods, and demonstrated the industrial clustering from perspectives of industrial organization and specialization theories.…”
Section: Introductionmentioning
confidence: 99%