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A consistent multivariate test of association based on ranks of distances

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TLDR
In this paper, the problem of detecting associations between random vectors of any dimension is considered and a powerful test that is applicable in all dimensions and consistent against all alternatives is proposed. But the test has a simple form, is easy to implement, and has good power.
Abstract
SUMMARY We consider the problem of detecting associations between random vectors of any dimension. Few tests of independence exist that are consistent against all dependent alternatives. We propose a powerful test that is applicable in all dimensions and consistent against all alternatives. The test has a simple form, is easy to implement, and has good power.

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Measuring dependence powerfully and equitably

TL;DR: In this article, a population measure of dependence called MIC* is introduced and characterized, and a new consistent estimator is defined for MIC* that is efficiently computable. But it is not known whether MIC* has better bias-variance properties than MIC.
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Screening for linearly and nonlinearly related variables in predictive cheminformatic models

TL;DR: An innovative method for selecting linearly and nonlineary correlated variables is presented, which works based on the hyphenation of nonparametric variable ranking methods with non parametric regression methods through an iterative regression based on residuals.
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OUP accepted manuscript

- 21 Feb 2022 - 
TL;DR: In this paper , the authors introduce a scalable, resampling-free approach to test the independence between two random vectors by breaking down the task into simple univariate tests of independence on a collection of $2\times 2$ contingency tables constructed through sequential coarse-to-fine discretization of the sample.
Posted Content

Discovering general multidimensional associations

TL;DR: This work demonstrates how to directly estimate a generalised R2 when the form of the relationship is unknown, and considers the performance of the Maximal Information Coefficient—a recently proposed information theoretic measure of dependence.
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Equitability, interval estimation, and statistical power

TL;DR: In this article, the authors define an equitable statistic as one with small interpretable intervals, which is a statistic that, given some measure of noise, assigns similar scores to equally noisy relationships of different types.
References
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Journal Article

R: A language and environment for statistical computing.

R Core Team
- 01 Jan 2014 - 
TL;DR: Copyright (©) 1999–2012 R Foundation for Statistical Computing; permission is granted to make and distribute verbatim copies of this manual provided the copyright notice and permission notice are preserved on all copies.
Journal ArticleDOI

The Analysis of Variance

TL;DR: In this paper, the basic theory of analysis of variance by considering several different mathematical models is examined, including fixed-effects models with independent observations of equal variance and other models with different observations of variance.
Journal ArticleDOI

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.
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Applied smoothing techniques for data analysis : the kernel approach with S-plus illustrations

TL;DR: 1. Density estimation for exploring data 2. D density estimation for inference 3. Nonparametric regression for explore data 4. Inference with nonparametric regressors 5. Checking parametric regression models 6. Comparing regression curves and surfaces
Journal ArticleDOI

The Analysis of Variance.

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