53,051 research outputs found
AN EXHAUSTIVE COEFFICIENT OF RANK CORRELATION
Rank association is a fundamental tool for expressing dependence in cases in which data are arranged in order. Measures of rank correlation have been accumulated in several contexts for more than a century and we were able to cite more than thirty of these coefficients, from simple ones to relatively complicated definitions invoking one or more systems of weights. However, only a few of these can actually be considered to be admissible substitutes for Pearson’s correlation. The main drawback with the vast majority of coefficients is their “resistance-tochange” which appears to be of limited value for the purposes of rank comparisons that are intrinsically robust. In this article, a new nonparametric correlation coefficient is defined that is based on the principle of maximization of a ratio of two ranks. In comparing it with existing rank correlations, it was found to have extremely high sensitivity to permutation patterns. We have illustrated the potential improvement that our index can provide in economic contexts by comparing published results with those obtained through the use of this new index. The success that we have had suggests that our index may have important applications wherever the discriminatory power of the rank correlation coefficient should be particularly strong.Ordinal data, Nonparametric agreement, Economic applications
Distribution-Free Tests of Independence in High Dimensions
We consider the testing of mutual independence among all entries in a
-dimensional random vector based on independent observations. We study
two families of distribution-free test statistics, which include Kendall's tau
and Spearman's rho as important examples. We show that under the null
hypothesis the test statistics of these two families converge weakly to Gumbel
distributions, and propose tests that control the type I error in the
high-dimensional setting where . We further show that the two tests are
rate-optimal in terms of power against sparse alternatives, and outperform
competitors in simulations, especially when is large.Comment: to appear in Biometrik
Brownian distance covariance
Distance correlation is a new class of multivariate dependence coefficients
applicable to random vectors of arbitrary and not necessarily equal dimension.
Distance covariance and distance correlation are analogous to product-moment
covariance and correlation, but generalize and extend these classical bivariate
measures of dependence. Distance correlation characterizes independence: it is
zero if and only if the random vectors are independent. The notion of
covariance with respect to a stochastic process is introduced, and it is shown
that population distance covariance coincides with the covariance with respect
to Brownian motion; thus, both can be called Brownian distance covariance. In
the bivariate case, Brownian covariance is the natural extension of
product-moment covariance, as we obtain Pearson product-moment covariance by
replacing the Brownian motion in the definition with identity. The
corresponding statistic has an elegantly simple computing formula. Advantages
of applying Brownian covariance and correlation vs the classical Pearson
covariance and correlation are discussed and illustrated.Comment: This paper discussed in: [arXiv:0912.3295], [arXiv:1010.0822],
[arXiv:1010.0825], [arXiv:1010.0828], [arXiv:1010.0836], [arXiv:1010.0838],
[arXiv:1010.0839]. Rejoinder at [arXiv:1010.0844]. Published in at
http://dx.doi.org/10.1214/09-AOAS312 the Annals of Applied Statistics
(http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics
(http://www.imstat.org
EEMCS final report for the causal modeling for air transport safety (CATS) project
This document reports on the work realized by the DIAM in relation to the completion of the CATS model as presented in Figure 1.6 and tries to explain some of the steps taken for its completion. The project spans over a period of time of three years. Intermediate reports have been presented throughout the project’s progress. These are presented in Appendix 1. In this report the continuous‐discrete distribution‐free BBNs are briefly discussed. The human reliability models developed for dealing with dependence in the model variables are described and the software application UniNet is presente
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