Related papers: Brownian sheet and uniformity tests on the hypercu…
The hypercontractive inequality on the discrete cube plays a crucial role in many fundamental results in the Analysis of Boolean functions, such as the KKL theorem, Friedgut's junta theorem and the invariance principle. In these results the…
Testing to see whether a given data set comes from some specified distribution is among the oldest types of problems in Statistics. Many such tests have been developed and their performance studied. The general result has been that while a…
We study quasi two-dimensional, monodisperse systems of active Brownian particles (ABPs) for a range of activities, stiffnesses, and densities. We develop a microscopic, analytical method for predicting the dense phase structure formed…
Trace monoids and heaps of pieces appear in various contexts in combinatorics. They also constitute a model used in computer science to describe the executions of asynchronous systems. The design of a natural probabilistic layer on top of…
There is currently a gap in theory for point patterns that lie on the surface of objects, with researchers focusing on patterns that lie in a Euclidean space, typically planar and spatial data. Methodology for planar and spatial data thus…
The celebrated union-closed conjecture is concerned with the cardinalities of various subsets of the Boolean $d$-cube. The cardinality of such a set is equivalent, up to a constant, to its measure under the uniform distribution, so we can…
We compare two examples of random dense countable sets, `Brownian local minima' and `unordered uniform infinite sample'. They appear to be identically distributed. A framework for such notions is proposed. In addition, random elements of…
We obtain sufficient conditions of stochastic equivalence of Gaussian random fields with special covariance function. These results generalize Doob's transformation (condition of stochastic equivalence of a Gaussian and a Wiener processes)…
When modeling directional data, that is, unit-norm multivariate vectors, a first natural question is to ask whether the directions are uniformly distributed or, on the contrary, whether there exist modes of variation significantly different…
We introduce a new randomization procedure for experiments based on the cube method, which achieves near-exact covariate balance. This ensures compliance with standard balance tests and allows for balancing on many covariates, enabling more…
In two recent papers [5] and [6], we generalized some classical results of Harmonic Analysis using probabilistic approach by means of a d- dimensional rotationally symmetric stable process. These results allow one to discuss some…
This paper considers testing linear hypotheses of a set of mean vectors with unequal covariance matrices in large dimensional setting. The problem of testing the hypothesis $H_0 : \sum_{i=1}^q \beta_i \bmu_i =\bmu_0 $ for a given vector…
We introduce a test of uniformity for (hyper)spherical data motivated by the stereographic projection. The closed-form expression of the test statistic and its null asymptotic distribution are derived using Gegenbauer polynomials. The power…
For large $n$, take a random $n \times n$ permutation matrix and its associated discrete copula $X_n$. For $a, b = 0, 1, \ldots, n$, let $y_n(\frac{a}{n},\frac{b}{n}) = \frac{1}{n} ( X_{a,b} - \frac{ab}{n} )$; define $y_n: [0,1]^2 \to R$ by…
We present new families of goodness-of-fit tests of uniformity on a full-dimensional set $W\subset\R^d$ based on statistics related to edge lengths of random geometric graphs. Asymptotic normality of these statistics is proven under the…
Aggregation patterns are often visually detected in sets of location data. These clusters may be the result of interesting dynamics or the effect of pure randomness. We build an asymptotically Gaussian test for the hypothesis of randomness…
Two procedures for checking Bayesian models are compared using a simple test problem based on the local Hubble expansion. Over four orders of magnitude, p-values derived from a global goodness-of-fit criterion for posterior probability…
We consider an empirical process based upon ratio of selected pair of the non-overlapping $m$-spacings generated by independent samples of arbitrary sizes. As a main result, we show that when both samples are uniformly distributed on…
Testing uniformity of a sample supported on the hypersphere is one of the first steps when analysing multivariate data for which only the directions (and not the magnitudes) are of interest. In this work, a projection-based Cram\'er-von…
The Brownian map is a random sphere-homeomorphic metric measure space obtained by "gluing together" the continuum trees described by the $x$ and $y$ coordinates of the Brownian snake. We present an alternative "breadth-first" construction…