Related papers: Time-uniform central limit theory and asymptotic c…
The global clustering coefficient serves as a powerful metric for the structural analysis and comparison of complex networks. Random geometric graphs offer a realistic framework for representing the spatial constraints and geometry often…
We consider sequences of symmetric $U$-statistics, not necessarily Hoeffding-degenerate, both in a one- and multi-dimensional setting, and prove quantitative central limit theorems (CLTs) based on the use of {\it contraction operators}. Our…
This paper studies large sample properties of a Bayesian approach to inference about slope parameters $\gamma$ in linear regression models with a structural break. In contrast to the conventional approach to inference about $\gamma$ that…
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 time series analysis, statistics based on collections of estimators computed from sub-samples play a crucial role in an increasing variety of important applications. Proving results about the joint asymptotic distribution of such…
The question of whether the central limit theorem (CLT) holds for the total number of edges in exponential random graph models (ERGMs) in the subcritical region of parameters has remained an open problem. In this paper, we establish the…
We consider Betti numbers of the excursion of a smooth Euclidean Gaussian field restricted to a rectangular window, in the asymptotics where the window grows to R^d . With motivations coming from Topological Data Analysis, we derive a…
General Central limit theorem deals with weak limits (in type) of sums of row-elements of array random variables. In some situations as in the invariance principle problem, the sums may include only parts of the row-elements. For strictly…
In this paper, we investigate the asymptotic stability of finite-dimensional stochastic integrable Hamiltonian systems via information entropy. Specifically, we establish the asymptotic vanishing of Shannon entropy difference (with…
Time series clustering promises to uncover hidden structural patterns in data with applications across healthcare, finance, industrial systems, and other critical domains. However, without validated ground truth information, researchers…
Higher criticism is a large-scale testing procedure that can attain the optimal detection boundary for sparse and faint signals. However, there has been a lack of knowledge in most existing works about its asymptotic distribution for more…
This paper investigates the central limit theorem for linear spectral statistics of high dimensional sample covariance matrices of the form $\mathbf{B}_n=n^{-1}\sum_{j=1}^{n}\mathbf{Q}\mathbf{x}_j\mathbf{x}_j^{*}\mathbf{Q}^{*}$ where…
This article establishes an asymptotic theory for volatility estimation in an infinite-dimensional setting. We consider mild solutions of semilinear stochastic partial differential equations and derive a stable central limit theorem for the…
A common statistical task lies in showing asymptotic normality of certain statistics. In many of these situations, classical textbook results on weak convergence theory suffice for the problem at hand. However, there are quite some…
In the paper [25], written in collaboration with Gesine Reinert, we proved a universality principle for the Gaussian Wiener chaos. In the present work, we aim at providing an original example of application of this principle in the…
Central limit theorems (CLTs) for high-dimensional random vectors with dimension possibly growing with the sample size have received a lot of attention in the recent times. Chernozhukov et al. (2017) proved a Berry--Esseen type result for…
Uniform convergence rates are provided for asymptotic representations of sample extremes. These bounds which are universal in the sense that they do not depend on the extreme value index are meant to be extended to arbitrary samples…
We prove an asymptotic stability result for a linear coupled hyperbolic-elliptic system on a large class of singular background spacetimes in CMC gauge on the n-torus. At each spatial point these background spacetimes are perturbations of…
Sample covariance matrices are widely used in multivariate statistical analysis. The central limit theorems (CLT's) for linear spectral statistics of high-dimensional non-centered sample covariance matrices have received considerable…
This paper discusses infill asymptotics for logistic regression estimators for spatio-temporal point processes whose intensity functions are of log-linear form. We establish strong consistency and asymptotic normality for the parameters of…