Related papers: Limit theorems of Chatterjee's rank correlation

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)…

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…

This paper re-examines the limit theorems of Abadie and Imbens for nearest-neighbor matching estimators of average treatment effects with a fixed number of matches. We establish, for the first time, a non-normalized central limit theorem…

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…

We consider asymptotic normality of linear rank statistics under various randomization rules met in clinical trials and designed for patients' allocation into treatment and placebo arms. Exposition relies on some general limit theorem due…

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…

The classical theory of rank-based inference is entirely based either on ordinary ranks, which do not allow for considering location (intercept) parameters, or on signed ranks, which require an assumption of symmetry. If the median, in the…

We consider the preferential attachment model. This is a growing random graph such that at each step a new vertex is added and forms $m$ connections. The neighbors of the new vertex are chosen at random with probability proportional to…

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…

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…

We suggest novel correlation coefficients which equal the maximum correlation for a class of bivariate Lancaster distributions while being only slightly smaller than maximum correlation for a variety of further bivariate distributions. In…

We provide an epsilon-delta interpretation of Chatterjee's rank correlation by tracing its origin to a notion of local dependence between random variables. Starting from a primitive epsilon-delta construction, we show that rank-based…

There is a substantial literature on testing for the equality of the cumulative incidence functions associated with one specific cause in a competing risks setting across several populations against specific or all alternatives. In this…

Under long memory, the limit theorems for normalized sums of random variables typically involve a positive integer called "Hermite rank". There is a different limit for each Hermite rank. From a statistical point of view, however, we argue…

Rank correlations have found many innovative applications in the last decade. In particular, suitable rank correlations have been used for consistent tests of independence between pairs of random variables. Using ranks is especially…

In order to address the theoretical challenges arising from the dependence structure of ranks in Spearman's footrule correlation coefficient, we propose two asymptotic representations to approximate the distribution of this coefficient…

We prove an almost sure weak limit theorem for simple linear rank statistics for samples with continuous distributions functions. As a corollary the result extends to samples with ties, and the vector version of an a.s. central limit…

We consider covariance asymptotics for linear statistics of general stationary random measures in terms of their truncated pair correlation measure. We give exact infinite series-expansion formulas for covariance of smooth statistics of…

We consider random graphs with a given degree sequence and show, under weak technical conditions, asymptotic normality of the number of components isomorphic to a given tree, first for the random multigraph given by the configuration model…

The Central Limit Theorem states that, in the limit of a large number of terms, an appropriately scaled sum of independent random variables yields another random variable whose probability distribution tends to a stable distribution. The…