Related papers: Limit theorems of Chatterjee's rank correlation
Nonparametric regression problems with qualitative constraints such as monotonicity or convexity are ubiquitous in applications. For example, in predicting the yield of a factory in terms of the number of labor hours, the monotonicity of…
Chatteerjee and Diaconis have recently shown the asymptotic normality for the joint distribution of the number of descents and inverse descents in a random permutation. A noteworthy point of their results is that the asymptotic variance of…
We study the isotonic regression estimator over a general countable pre-ordered set. We obtain the limiting distribution of the estimator and study its properties. It is proved that, under some general assumptions, the limiting distribution…
Often of primary interest in the analysis of multivariate data are the copula parameters describing the dependence among the variables, rather than the univariate marginal distributions. Since the ranks of a multivariate dataset are…
We study conditions under which treatment effect estimators constructed under the no-interference assumption in randomized experiments are asymptotically normal in the presence of interference. We prove that the standard Horvitz-Thompson…
The Central Limit Theorem (CLT) is one of the most fundamental results in statistics. It states that the standardized sample mean of a sequence of $n$ mutually independent and identically distributed random variables with finite first and…
The focus of this work is the asymptotic analysis of the tail distribution of Google's PageRank algorithm on large scale-free directed networks. In particular, the main theorem provides the convergence, in the Kantorovich-Rubinstein metric,…
We introduce the coverage correlation coefficient, a novel nonparametric measure of statistical association designed to quantifies the extent to which two random variables have a joint distribution concentrated on a singular subset with…
In this article we discuss estimation of the common variance of several normal populations with tree order restricted means. We discuss the asymptotic properties of the maximum likelihood estimator of the variance as the number of…
This paper is concerned with the limiting spectral behaviors of large dimensional Kendall's rank correlation matrices generated by samples with independent and continuous components. We do not require the components to be identically…
In this paper the asymptotic distribution of estimators is derived in a general regression setting where rank restrictions on a submatrix of the coefficient matrix are imposed and the regressors can include stationary or I(1) processes.…
This paper systematically studies the behavior of the leading eigenvectors for independent edge undirected random graphs generated from a general latent position model whose link function is possibly infinite rank and also possibly…
For a uniform random labelled tree, we find the limiting distribution of tree parameters which are stable (in some sense) with respect to local perturbations of the tree structure. The proof is based on the martingale central limit theorem…
Let $\FF$ be an arbitrary field and $(\bm{G}_{n,d/n})_n$ be a sequence of sparse weighted Erd\H{o}s-R\'enyi random graphs on $n$ vertices with edge probability $d/n$, where weights from $\FF \setminus\{0\}$ are assigned to the edges…
We study the asymptotic behavior of the rank statistic for unimodal sequences. We use analytic techniques involving asymptotic expansions in order to prove asymptotic formulas for the moments of the rank. Furthermore, when appropriately…
A key feature of a sequential study is that the actual sample size is a random variable that typically depends on the outcomes collected. While hypothesis testing theory for sequential designs is well established, parameter and precision…
We analyze the properties of matching estimators when there are few treated, but many control observations. We show that, under standard assumptions, the nearest neighbor matching estimator for the average treatment effect on the treated is…
We determine the asymptotic distribution of the sum of correlated variables described by a matrix product ansatz with finite matrices, considering variables with finite variances. In cases when the correlation length is finite, the law of…
Many enumeration problems in combinatorics, including such fundamental questions as the number of regular graphs, can be expressed as high-dimensional complex integrals. Motivated by the need for a systematic study of the asymptotic…
We study the asymptotic properties of distributed consensus algorithms over switching directed random networks. More specifically, we focus on consensus algorithms over independent and identically distributed, directed random graphs, where…