Related papers: Two-Sample U-Statistic Processes for Long-Range De…
We consider the \mnk{classical} problem of a controller activating (or sampling) sequentially from a finite number of $N \geq 2$ populations, specified by unknown distributions. Over some time horizon, at each time $n = 1, 2, \ldots$, the…
Let $\{X_i(t),t\ge0\}, 1\le i\le n$ be independent centered stationary Gaussian processes with unit variance and almost surely continuous sample paths. For given positive constants $u,T$, define the set of conjunctions $C_{[0,T],u}:=\{t\in…
In a celebrated paper, Dyson shows that the spectrum of an n\times n random Hermitian matrix, diffusing according to an Ornstein-Uhlenbeck process, evolves as n noncolliding Brownian motions held together by a drift term. The universal edge…
In this monograph, we prove an asymptotic approximation for integrals of probability densities over sets in finite dimensional euclidean space, which are far away from the origin (asymptotic sets). We use this approximation to investigate…
In this article, we propose a class of test statistics for a change point in the mean of high-dimensional independent data. Our test integrates the U-statistic based approach in a recent work by \cite{hdcp} and the $L_q$-norm based…
In this paper, we propose a test for the equality of multiple distributions based on kernel mean embeddings. Our framework provides a flexible way to handle multivariate or even high-dimensional data by virtue of kernel methods and allows…
Scaling limits for continuous-time branching processes with discrete state space are provided as the initial state tends to infinity. Depending on the finiteness or non-finiteness of the mean and/or the variance of the offspring…
We study Hermitian random matrix models with an external source matrix which has equispaced eigenvalues, and with an external field such that the limiting mean density of eigenvalues is supported on a single interval as the dimension tends…
High-dimensional changepoint inference that adapts to various change patterns has received much attention recently. We propose a simple, fast yet effective approach for adaptive changepoint testing. The key observation is that two…
We provide a distribution-free test that can be used to determine whether any two joint distributions $p$ and $q$ are statistically different by inspection of a large enough set of samples. Following recent efforts from Long et al. [1], we…
We present a novel approach to test for heteroscedasticity of a non-stationary time series that is based on Gini's mean difference of logarithmic local sample variances. In order to analyse the large sample behaviour of our test statistic,…
To detect a changed segment (so called epidemic changes) in a time series, variants of the CUSUM statistic are frequently used. However, they are sensitive to outliers in the data and do not perform well for heavy tailed data, especially…
This paper presents the asymptotic theory for nondegenerate $U$-statistics of high frequency observations of continuous It\^{o} semimartingales. We prove uniform convergence in probability and show a functional stable central limit theorem…
The convergence of a sequence of point processes with dependent points, defined by a symmetric function of iid high-dimensional random vectors, to a Poisson random measure is proved. This also implies the convergence of the joint…
We derive asymptotic expansions of the Kummer functions $M(a,b,z)$ and $U(a,b+1,z)$ for large positive values of $a$ and $b$, with $z$ fixed. For both functions we consider $b/a\le 1$ and $b/a\ge 1$, with special attention for the case…
The Renyi, Shannon and Fisher spreading lengths of the classical or hypergeometric orthogonal polynomials, which are quantifiers of their distribution all over the orthogonality interval, are defined and investigated. These…
As well as arising naturally in the study of non-intersecting random paths, random spanning trees, and eigenvalues of random matrices, determinantal point processes (sometimes also called fermionic point processes) are relatively easy to…
In modern data analysis, nonparametric measures of discrepancies between random variables are particularly important. The subject is well-studied in the frequentist literature, while the development in the Bayesian setting is limited where…
In this work, we introduce statistical testing under distributional shifts. We are interested in the hypothesis $P^* \in H_0$ for a target distribution $P^*$, but observe data from a different distribution $Q^*$. We assume that $P^*$ is…
Standard regression approaches assume that some finite number of the response distribution characteristics, such as location and scale, change as a (parametric or nonparametric) function of predictors. However, it is not always appropriate…