Related papers: Central Limit Theorem and the Bootstrap for U-Stat…
We continue our study of the defect CFT on a Maldacena-Wilson line in N=4 Super-Yang-Mills theory using Bootstrability -- the conformal bootstrap supplemented with exact integrability data. In this paper, we extend this program to charged…
Given a dataset an outlier can be defined as an observation that it is unlikely to follow the statistical properties of the majority of the data. Computation of the location estimate of is fundamental in data analysis, and it is well known…
This paper introduces a universal approach to seamlessly combine out-of-distribution (OOD) detection scores. These scores encompass a wide range of techniques that leverage the self-confidence of deep learning models and the anomalous…
In this paper, we consider a framework adapting the notion of cointegration when two asset prices are generated by a driftless It\^{o}-semimartingale featuring jumps with infinite activity, observed regularly and synchronously at high…
Linear structural error-in-variables models with univariate observations are revisited for studying modified least squares estimators of the slope and intercept. New marginal central limit theorems (CLT's) are established for these…
Recently there has been much interest in data that, in statistical language, may be described as having a large crossed and severely unbalanced random effects structure. Such data sets arise for recommender engines and information retrieval…
We prove the claim in the title under mild conditions which are usually satisfied when trying to establish asymptotic normality. We assume strictly stationary and absolutely regular data.
When we use the normal mixture model, the optimal number of the components describing the data should be determined. Testing homogeneity is good for this purpose; however, to construct its theory is challenging, since the test statistic…
A notion of local $U$-statistic process is introduced and central limit theorems in various norms are obtained for it. This involves the development of several inequalities for $U$-processes that may be useful in other contexts. This local…
One of the most commonly used methods for forming confidence intervals for statistical inference is the empirical bootstrap, which is especially expedient when the limiting distribution of the estimator is unknown. However, despite its…
We prove a convergence theorem for U-statistics of degree two, where the data dimension $d$ is allowed to scale with sample size $n$. We find that the limiting distribution of a U-statistic undergoes a phase transition from the…
Let (S_n)_{n\in\N} be a Z-valued random walk with increments from the domain of attraction of some \alpha-stable law and let (\xi(i))_{i\in\Z} be a sequence of iid random variables. We want to investigate U-statistics indexed by the random…
In this paper, quantitative bounds in high-frequency central limit theorems are derived for Poisson based $U$-statistics of arbitrary degree built by means of wavelet coefficients over compact Riemannian manifolds. The wavelets considered…
Two-sample $U$-statistics are widely used in a broad range of applications, including those in the fields of biostatistics and econometrics. In this paper, we establish sharp Cram\'{e}r-type moderate deviation theorems for Studentized…
We prove a central limit theorem (CLT) for the number of joint orbits of random tuples of commuting permutations. In the uniform sampling case this generalizes the classic CLT of Goncharov for the number of cycles of a single random…
In this paper we extend a central limit theorem of Peligrad for uniformly strong mixing random fields satisfying the Lindeberg condition in the absence of stationarity property. More precisely, we study the asymptotic normality of the…
Unsupervised anomaly detection (AD) is a fundamental problem in machine learning and statistics. A popular approach to unsupervised AD is clustering-based detection. However, this method lacks the ability to guarantee the reliability of the…
Although there is an extensive literature on the eigenvalues of high-dimensional sample covariance matrices, much of it is specialized to independent components (IC) models -- in which observations are represented as linear transformations…
Graph clustering is a fundamental task in unsupervised learning with broad real-world applications. While spectral clustering methods for undirected graphs are well-established and guided by a minimum cut optimization consensus, their…
We study the conformal bootstrap for systems of correlators involving non-identical operators. The constraints of crossing symmetry and unitarity for such mixed correlators can be phrased in the language of semidefinite programming. We…