Related papers: Two-Sample U-Statistic Processes for Long-Range De…
In descriptive statistics, $U$-statistics arise naturally in producing minimum-variance unbiased estimators. In 1984, Serfling considered the distribution formed by evaluating the kernel of the $U$-statistics and proposed generalized…
In machine learning, we are given a dataset of the form $\{(\mathbf{x}_j,y_j)\}_{j=1}^M$, drawn as i.i.d. samples from an unknown probability distribution $\mu$; the marginal distribution for the $\mathbf{x}_j$'s being $\mu^*$. We propose…
In this work we study the properties of segregation processes modeled by a family of equations $$ L(u_i) (x) = u_i(x)\: F_i (u_1, \ldots, u_K)(x)\qquad i=1,\ldots, K $$ where $F_i (u_1, \ldots, u_K)(x)$ is a non-local factor that takes into…
We investigate a generalized empirical likelihood approach in a two-group setting where the constraints on parameters have a form of U-statistics. In this situation, the summands that consist of the constraints for the empirical likelihood…
Classical asymptotic theory for statistical inference usually involves calibrating a statistic by fixing the dimension $d$ while letting the sample size $n$ increase to infinity. Recently, much effort has been dedicated towards…
In this paper we propose the use of $\phi$-divergences as test statistics to verify simple hypotheses about a one-dimensional parametric diffusion process $\de X_t = b(X_t, \theta)\de t + \sigma(X_t, \theta)\de W_t$, from discrete…
Let $\{X_{n}(t), t\in[0,\infty)\}, n\in\mathbb{N}$ be a sequence of centered dependent stationary Gaussian processes. The limit distribution of $\sup_{t\in[0,T(n)]}|X_{n}(t)|$ is established as $r_{n}(t)$, the correlation function of…
We consider change-point tests based on rank statistics to test for structural changes in long-range dependent observations. Under the hypothesis of stationary time series and under the assumption of a change with decreasing change-point…
Testing the equality of two conditional distributions is crucial in various modern applications, including transfer learning and causal inference. Despite its importance, this fundamental problem has received surprisingly little attention…
Answering a question of Clark and Ehrenborg (2010), we determine asymptotics for the number of permutations of size n that admit the most common excedance set. In fact, we provide a more general bivariate asymptotic using the multivariate…
The goal of this paper is to quantitatively describe some statistical properties of higher-dimensional determinantal point processes with a primary focus on the nearest-neighbor distribution functions. Toward this end, we express these…
We study the asymptotic behavior of the fluctuations of smooth and rough linear statistics for determinantal point processes on the sphere and on the Euclidean space. The main tool is the generalization of some norm representation results…
We propose a class of nonparametric two-sample tests with a cost linear in the sample size. Two tests are given, both based on an ensemble of distances between analytic functions representing each of the distributions. The first test uses…
Asymptotic expansions for a wide class of distribution are studied. A simple method for computation of the series coefficients is suggested. The case when regularization parameter of the distribution depends on the asymptotic parameter is…
For a sample of Exponentially distributed durations we aim at point estimation and a confidence interval for its parameter. A duration is only observed if it has ended within a certain time interval, determined by a Uniform distribution.…
This paper provides a precise error analysis for the maximum likelihood estimate $\hat{a}_{\text{ML}}(u_1^n)$ of the parameter $a$ given samples $u_1^n = (u_1, \ldots, u_n)'$ drawn from a nonstationary Gauss-Markov process $U_i = a U_{i-1}…
The use of an Ornstein-Uhlenbeck (OU) process is ubiquitous in business, economics and finance to capture various price processes and evolution of economic indicators exhibiting mean-reverting properties. When structural changes happen,…
While short-range dependence is widely assumed in the literature for its simplicity, long-range dependence is a feature that has been observed in data from finance, hydrology, geophysics and economics. In this paper, we extend a…
We apply the concept of distance covariance for testing independence of two long-range dependent time series. As test statistic we propose a linear combination of empirical distance cross-covariances. We derive the asymptotic distribution…
We establish a convergent power series expansion for the expectation of a product of traces of powers of a random unitary matrix under the heat kernel measure. These expectations turn out to be the generating series of certain paths in the…