Related papers: On Rank Correlation Coefficients
Estimating the correlation coefficient has been a daunting work with the increasing complexity of dataset's pattern. One of the problems in manufacturing applications consists of the estimation of a critical process variable during a…
This paper analyzes the performances of the Spearman's rho (SR) and Kendall's tau (KT) with respect to samples drawn from bivariate normal and bivariate contaminated normal populations. The exact analytical formulae of the variance of SR…
Independence screening is a variable selection method that uses a ranking criterion to select significant variables, particularly for statistical models with nonpolynomial dimensionality or "large p, small n" paradigms when p can be as…
The Pearson correlation coefficient is commonly used for quantifying the global level of degree-degree association in complex networks. Here, we use a probabilistic representation of the underlying network structure for assessing the…
In this paper, we develop a local rank correlation measure which quantifies the performance of dimension reduction methods. The local rank correlation is easily interpretable, and robust against the extreme skewness of nearest neighbor…
In this paper, we establish a new inequality tying together the effective length and the maximum correlation between the outputs of an arbitrary pair of Boolean functions which operate on two sequences of correlated random variables. We…
The rank-based association between two variables can be modeled by introducing a latent normal level to ordinal data. We demonstrate how this approach yields Bayesian inference for Kendall's rank correlation coefficient, improving on a…
We propose a coefficient that measures dependence in paired samples of functions. It has properties similar to the Pearson correlation, but differs in significant ways: (i) it is designed to measure dependence between curves, (ii) it…
Herein, we propose a Spearman rank correlation based screening procedure for ultrahigh-dimensional data with censored response case. The proposed method is model-free without specifying any regression forms of predictors or response…
Recently, Chatterjee has introduced a new coefficient of correlation which has several natural properties. In particular, the coefficient attains its maximal value if and only if one variable is a measurable function of the other variable.…
The relation between Pearson's correlation coefficient and Salton's cosine measure is revealed based on the different possible values of the division of the L1-norm and the L2-norm of a vector. These different values yield a sheaf of…
A fundamental problem in statistics is measuring the correlation between two rankings of a set of items. Kendall's $\tau$ and Spearman's $\rho$ are well established correlation coefficients whose symmetric structure guarantees zero expected…
In network theory, Pearson's correlation coefficients are most commonly used to measure the degree assortativity of a network. We investigate the behavior of these coefficients in the setting of directed networks with heavy-tailed degree…
We introduce a new type of influence function, the asymptotic expected sensitivity function, which is often equivalent to but mathematically more tractable than the traditional one based on the Gateaux derivative. To illustrate, we study…
The advent of modern data collection and processing techniques has seen the size, scale, and complexity of data grow exponentially. A seminal step in leveraging these rich datasets for downstream inference is understanding the…
In his seminal work, Chatterjee (2021) introduced a novel correlation measure which is distribution-free, asymptotically normal, and consistent against all alternatives. In this paper, we study the probabilistic relationships between…
While measures of concordance -- such as Spearman's rho, Kendall's tau, and Blomqvist's beta -- are continuous with respect to weak convergence, Chatterjee's rank correlation xi recently introduced in Azadkia and Chatterjee (2021) does not…
In statistical classification and machine learning, as well as in social and other sciences, a number of measures of association have been proposed for assessing and comparing individual classifiers, raters, as well as their groups. In this…
Kemeny (1959) introduced a topologically complete metric space to study ordinal random variables, particularly in the context of Condorcet's paradox and the measurability of ties. Building on this, Emond & Mason (2002) reformulated Kemeny's…
In this paper, we propose a novel Euclidean-distance-based coefficient, named differential distance correlation, to measure the strength of dependence between a random variable $ Y \in \mathbb{R} $ and a random vector $ \boldsymbol{X} \in…