Related papers: Bias correction for Chatterjee's graph-based corre…
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…
Azadkia and Chatterjee (Azadkia and Chatterjee, 2021) recently introduced a graph-based correlation coefficient that has garnered significant attention. The method relies on a nearest neighbor graph (NNG) constructed from the data. While…
In their seminal work, Azadkia and Chatterjee (2021) initiated graph-based methods for measuring variable dependence strength. By appealing to nearest neighbor graphs, they gave an elegant solution to a problem of R\'enyi (R\'enyi, 1959).…
Recently, Chatterjee (2021) introduced a new rank-based correlation coefficient which can be used to measure the strength of dependence between two random variables. This coefficient has already attracted much attention as it converges to…
Chatterjee (2021)'s ingenious approach to estimating a measure of dependence first proposed by Dette et al. (2013) based on simple rank statistics has quickly caught attention. This measure of dependence has the unusual property of being…
We extend the scope of Azadkia-Chatterjee's dependence coefficient between a scalar response $Y$ and a multivariate covariate $X$ to the case where $X$ takes values in a general metric space. Particular attention is paid to the case where…
In recent work, Azadkia and Chatterjee (2021) laid out an ingenious approach to defining consistent measures of conditional dependence. Their fully nonparametric approach forms statistics based on ranks and nearest neighbor graphs. 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…
Dette, Siburg, and Stoimenov (2013) introduced a copula-based measure of dependence, which implies independence if it vanishes and is equal to 1 if one variable is a measurable function of the other. For continuous distributions, the…
Chatterjee's correlation coefficient has recently been proposed as a new association measure for bivariate random vectors that satisfies a number of desirable properties. Among these properties is the feature that the coefficient equals one…
Recently, Chatterjee (2023) recognized the lack of a direct generalization of his rank correlation $\xi$ in Azadkia and Chatterjee (2021) to a multi-dimensional response vector. As a natural solution to this problem, we here propose an…
The Azadkia-Chatterjee coefficient is a rank-based measure of dependence between a random variable $Y \in \mathbb{R}$ and a random vector ${\boldsymbol Z} \in \mathbb{R}^{d_Z}$. In this paper, we propose a multivariate extension that…
While researchers commonly use the bootstrap for statistical inference, many of us have realized that the standard bootstrap, in general, does not work for Chatterjee's rank correlation. In this paper, we provide proof of this issue under…
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…
Chatterjee (2021) introduced an asymmetric correlation measure that has attracted much attention over the past year. In this paper, we derive the asymptotic distribution of the symmetric version of Chatterjee's correlation, and suggest a…
Chatterjee's rank correlation is a directed measure of association designed to detect whether one variable can be predicted as a function of another. While the original coefficient is naturally defined for real-valued data, circular data…
We prove that a suitably de-biased version of Chatterjee's rank correlation based on i.i.d. copies of a random vector $(X,Y)$ is asymptotically normal whenever $Y$ is not almost surely constant. No further conditions on the joint…
Estimating some mathematical expectations from partially observed data and in particular missing outcomes is a central problem encountered in numerous fields such as transfer learning, counterfactual analysis or causal inference. Matching…
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)…
Building upon the Chatterjee correlation (2021: J. Am. Stat. Assoc. 116, p2009) for two real-valued variables, this study introduces a generalized measure of directed association between two vector variables, real or complex-valued, and of…