Brownian distance covariance

Székely, Gábor; Rizzo, Maria L.

doi:10.1214/09-aoas312

Cited by 662 publications

(602 citation statements)

References 20 publications

(23 reference 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.…”

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confidence: 99%

Using distance correlation and SS-ANOVA to assess associations of familial relationships, lifestyle factors, diseases, and mortality

Kong¹,

Klein

et al. 2012

Proc. Natl. Acad. Sci. U.S.A.

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We present a method for examining mortality as it is seen to run in families, and lifestyle factors that are also seen to run in families, in a subpopulation of the Beaver Dam Eye Study. We observe that pairwise distance between death age in related persons is on average less than pairwise distance in death age between random pairs of unrelated persons. Our goal is to examine the hypothesis that pairwise differences in lifestyle factors correlate with the observed pairwise differences in death age that run in families. Szekely and Rizzo [Szekely GJ, Rizzo ML (2009) Ann Appl Stat 3(4): 1236–1265] have recently developed a method called distance correlation, which is suitable for this task with some enhancements. We build a Smoothing Spline ANOVA (SS-ANOVA) model for predicting death age based on four major lifestyle factors generally known to be related to mortality and four major diseases contributing to mortality, to develop a lifestyle mortality risk vector and a disease mortality risk vector. We then examine to what extent pairwise differences in these scores correlate with pairwise differences in mortality as they occur between family members and between unrelated persons. We find significant distance correlations between death ages, lifestyle factors, and family relationships. Considering only sib pairs compared with unrelated persons, distance correlation between siblings and mortality is, not surprisingly, stronger than that between more distantly related family members and mortality. The methodological approach here adapts to exploring relationships between multiple clusters of variables with observable (real-valued) attributes, and other factors for which only possibly nonmetric pairwise dissimilarities are observed.

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confidence: 99%

Using distance correlation and SS-ANOVA to assess associations of familial relationships, lifestyle factors, diseases, and mortality

Kong¹,

Klein

et al. 2012

Proc. Natl. Acad. Sci. U.S.A.

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“…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%

Model-Free Feature Screening for Ultrahigh Dimensional Data through a Modified Blum-Kiefer-Rosenblatt Correlation

Zhu¹,

Zhou²

2018

STAT SINICA

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In this paper we introduce a modified Blum-Kiefer-Rosenblatt correlation (MBKR for short) to rank the relative importance of each predictor in ultrahigh dimensional regressions. We advocate using the MBKR for two reasons. First, the MBKR is nonnegative and equals zero if and only if two random variables are independent, indicating that the MBKR can detect nonlinear dependence. We illustrate that the sure independence screening procedure based on the MBKR (MBKR-SIS for short) is effective to detect nonlinear effects including interactions and heterogeneity, particularly when both continuous and discrete predictors are involved simultaneously. Second, the MBKR is conceptually simple, easy to implement and affine-invariant. The MBKR is free of tuning parameters and no iteration is required in estimation. It remains unchanged when order-preserving transformations are applied to the response or predictors, indicating that the MBKR-SIS is robust to the presence of extreme values and outliers in the observations. We also show that, under mild conditions, the MBKR-SIS procedure has the desirable sure screening and ranking consistency properties, Statistica Sinica: Newly accepted Paper (accepted version subject to English editing) Feature Screening via Modified Blum-Kiefer-Rosenblatt Correlation 2 which guarantee that all important predictors can be retained after screening with probability approaching one. We also propose an iterative screening procedure to detect the important predictors which are marginally independent of the response variable. We demonstrate the merits of the MBKR-SIS procedure through simulations and an application to a real-world dataset.

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“…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%

A Study of the Transfer Entropy Networks on Industrial Electricity Consumption

Yao

Kuang

Lin

et al. 2017

Entropy

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Abstract:We study information transfer routes among cross-industry and cross-region electricity consumption data based on transfer entropy and the MST (Minimum Spanning Tree) model. First, we characterize the information transfer routes with transfer entropy matrixes, and find that the total entropy transfer of the relatively developed Guangdong Province is lower than others, with significant industrial cluster within the province. Furthermore, using a reshuffling method, we find that driven industries contain much more information flows than driving industries, and are more influential on the degree of order of regional industries. Finally, based on the Chu-Liu-Edmonds MST algorithm, we extract the minimum spanning trees of provincial industries. Individual MSTs show that the MSTs follow a chain-like formation in developed provinces and star-like structures in developing provinces. Additionally, all MSTs with the root of minimal information outflow industrial sector are of chain-form.

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Brownian distance covariance

Cited by 662 publications

References 20 publications

Using distance correlation and SS-ANOVA to assess associations of familial relationships, lifestyle factors, diseases, and mortality

Using distance correlation and SS-ANOVA to assess associations of familial relationships, lifestyle factors, diseases, and mortality

Model-Free Feature Screening for Ultrahigh Dimensional Data through a Modified Blum-Kiefer-Rosenblatt Correlation

A Study of the Transfer Entropy Networks on Industrial Electricity Consumption

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