The distance correlation t-test of independence in high dimension
Gábor J. Székely,Maria L. Rizzo +1 more
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TLDR
A modified distance correlation statistic is proposed, such that under independence the distribution of a transformation of the statistic converges to Student t, as dimension tends to infinity, and the resulting t-test is unbiased for every sample size greater than three and all significance levels.About:
This article is published in Journal of Multivariate Analysis.The article was published on 2013-05-01 and is currently open access. It has received 287 citations till now. The article focuses on the topics: Distance correlation & Correlation dimension.read more
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Energy statistics: A class of statistics based on distances
TL;DR: Energy distance is a statistical distance between the distributions of random vectors, which characterizes equality of distributions as mentioned in this paper, and there is an elegant relation to the notion of potential energy between statistical observations.
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Partial distance correlation with methods for dissimilarities
Gábor J. Székely,Maria L. Rizzo +1 more
TL;DR: In this paper, the authors define the partial distance correlation statistics with the help of a new Hilbert space, and develop and implement a test for zero partial distance correlations, and provide an unbiased estimator of squared distance covariance, and a neat solution to the problem of distance correlation for dissimilarities rather than distances.
Journal ArticleDOI
Energy distance
Maria L. Rizzo,Gábor J. Székely +1 more
TL;DR: Applications include testing independence by distance covariance, goodness‐of‐fit, nonparametric tests for equality of distributions and extension of analysis of variance, generalizations of clustering algorithms, change point analysis, feature selection, and more.
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Challenges in measuring individual differences in functional connectivity using fMRI: The case of healthy aging.
TL;DR: It is shown that analysis choices have a dramatic impact on connectivity differences between individuals, ultimately affecting the associations found between connectivity and cognition, and a number of ways to optimize analysis choices are suggested.
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Global sensitivity analysis with dependence measures
TL;DR: In this article, a new class of sensitivity indices based on dependence measures is introduced, which overcomes the theoretical and practical limitations of global sensitivity analysis with variance-based measures, since they focus only on the variance of the output and handle multivariate variables in a limited way.
References
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Measuring and testing dependence by correlation of distances
TL;DR: Distance correlation is a new measure of dependence between random vectors that is based on certain Euclidean distances between sample elements rather than sample moments, yet has a compact representation analogous to the classical covariance and correlation.