Related papers: On the Kendall Correlation Coefficient
Machine learning classification tasks often benefit from predicting a set of possible labels with confidence scores to capture uncertainty. However, existing methods struggle with the high-dimensional nature of the data and the lack of…
This article proposes an improved version of the Spearman rank correlation based on using Wilcoxon rank score function. A smoothed empirical cumulative distribution function (ecdf)computes the smoothed ranks and replaces the regular ranks…
This paper introduces the correlation-of-divergency coefficient, c-delta, a custom statistical measure designed to quantify the similarity of internal divergence patterns between two groups of values. Unlike conventional correlation…
Distance correlation is a measure of dependence between two paired random vectors or matrices of arbitrary, not necessarily equal, dimensions. Unlike Pearson correlation, the population distance correlation coefficient is zero if and only…
In statistics, the Pearson correlation coefficient $r_{x,y}$ determines the degree of linear correlation between two variables and it is known that $-1 \le r_{x,y} \le 1$. In the theory of networks, a curious expression proposed in [PRL…
Chatterjee's rank correlation coefficient $\xi_n$ is an empirical index for detecting functional dependencies between two variables $X$ and $Y$. It is an estimator for a theoretical quantity $\xi$ that is zero for independence and one if…
In this paper, we address the problem of testing independence between two high-dimensional random vectors. Our approach involves a series of max-sum tests based on three well-known classes of rank-based correlations. These correlation…
Multiple correlation is a fundamental concept with broad applications. The classical multiple correlation coefficient is developed to assess how strongly a dependent variable is associated with a linear combination of independent variables.…
Chatterjee (2021) introduced a simple new rank correlation coefficient that has attracted much recent attention. The coefficient has the unusual appeal that it not only estimates a population quantity first proposed by Dette et al. (2013)…
The Pearson correlation, correlation ratio, and maximal correlation have been well-studied in the literature. In this paper, we study the conditional versions of these quantities. We extend the most important properties of the unconditional…
A new class of general exponential ranking models is introduced which we label angle-based models for ranking data. A consensus score vector is assumed, which assigns scores to a set of items, where the scores reflect a consensus view of…
Kendall's tau and Spearman's rho are widely used tools for measuring dependence. Surprisingly, when it comes to asymptotic inference for these rank correlations, some fundamental results and methods have not yet been developed, in…
Joint modeling of a large number of variables often requires dimension reduction strategies that lead to structural assumptions of the underlying correlation matrix, such as equal pair-wise correlations within subsets of variables. The…
Establishing the limiting distribution of Chatterjee's rank correlation for a general, possibly non-independent, pair of random variables has been eagerly awaited by many. This paper shows that (a) Chatterjee's rank correlation is…
The comparison of alternative rankings of a set of items is a general and prominent task in applied statistics. Predictor variables are ranked according to magnitude of association with an outcome, prediction models rank subjects according…
For nonnegative random variables with finite means we introduce an analogous of the equilibrium residual-lifetime distribution based on the quantile function. This allows to construct new distributions with support (0,1), and to obtain a…
The partial correlation coefficient is a commonly used measure to assess the conditional dependence between two random variables. We provide a thorough explanation of the partial copula, which is a natural generalization of the partial…
A version of the secretary problem is considered. The ranks of items, whose values are independent, identically distributed random variables $X_1,X_2,...,X_n$ from a uniform distribution on $[0; 1]$, are observed sequentially by the grader.…
Distance correlation is a recent extension of Pearson's correlation, that characterises general statistical independence between Euclidean-space-valued random variables, not only linear relations. This review delves into how and when…
Feature screening is useful and popular to detect informative predictors for ultrahigh-dimensional data before developing proceeding statistical analysis or constructing statistical models. While a large body of feature screening procedures…