Related papers: Brownian sheet and uniformity tests on the hypercu…

We provide a new construction of Brownian disks in terms of forests of continuous random trees equipped with nonnegative labels corresponding to distances from a distinguished point uniformly distributed on the boundary of the disk. This…

Over the last couple of decades, several copula based methods have been proposed in the literature to test for the independence among several random variables. But these existing tests are not invariant under monotone transformations of the…

We study the topology of a random cubical complex associated to Bernoulli site percolation on a cubical grid. We begin by establishing a limit law for homotopy types. More precisely, looking within an expanding window, we define a sequence…

Uniform large deviation principles for positive functionals of all equivalent types of infinite dimensional Brownian motions acting together with a Poisson random measure are established. The core of our approach is a variational…

Motivated by the likelihood ratio test under the Gaussian assumption, we develop a maximum sum-of-squares test for conducting hypothesis testing on high dimensional mean vector. The proposed test which incorporates the dependence among the…

Hypothesis tests in models whose dimension far exceeds the sample size can be formulated much like the classical studentized tests only after the initial bias of estimation is removed successfully. The theory of debiased estimators can be…

We introduce and study a new random surface which we call the hyperbolic Brownian plane and which is the near-critical scaling limit of the hyperbolic triangulations constructed in arXiv:1401.3297. The law of the hyperbolic Brownian plane…

A popular approach for testing if two univariate random variables are statistically independent consists of partitioning the sample space into bins, and evaluating a test statistic on the binned data. The partition size matters, and the…

In this paper, we propose several statistics for testing uniformity under progressive Type-I interval censoring. We obtain the critical points of these statistics and study the power of the proposed tests against a representative set of…

We study the behaviour of a Brownian particle in the overdamped regime in the presence of a harmonic potential, assuming its diffusion coefficient to randomly jump between two distinct values. In particular, we characterize the probability…

While quantum speed-up in solving certain decision problems by a fault-tolerant universal quantum computer has been promised, a timely research interest includes how far one can reduce the resource requirement to demonstrate a provable…

We present results from a series of experiments on a granular medium sheared in a Couette geometry and show that their statistical properties can be computed in a quantitative way from the assumption that the resultant from the set of…

The empirical copula process, a fundamental tool for copula inference, is studied in the high dimensional regime where the dimension is allowed to grow to infinity exponentially in the sample size. Under natural, weak smoothness assumptions…

In this paper we propose and examine gap statistics for assessing uniform distribution hypotheses. We provide examples relevant to data integrity testing for which max-gap statistics provide greater sensitivity than chi-square ($\chi^2$),…

Experimental data from axially symmetric compression test at constant mean pressure p on Hostun sand from Bouvard experiments are used to study the validity of an "isotropic" modelling as a function of the density .The isotropic assumption…

Verifying uniform conditions over continuous spaces through random sampling is fundamental in machine learning and control theory, yet classical coverage analyses often yield conservative bounds, particularly at small failure probabilities.…

A single parameter cubic composite test for odd positive integers is given which relies on the discriminant always being a square integer. This test has no known counterexample despite extensive verifications. As well as a comparison with…

We consider large uniform labeled random graphs in different classes with prescribed decorations in their modular decomposition. Our main result is the estimation of the number of copies of every graph as an induced subgraph. As a…

A test of uniformity on [0,1] is developed for the setting of a single observation recorded with sufficient precision. Although consistency against general alternatives is not attainable with only one draw in the classical large-sample…

In this paper, we present a new classifier, which integrates significance testing results over different random subspaces to yield consensus p-values for quantifying the uncertainty of classification decision. The null hypothesis is that…