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

We consider a multivariate piecewise linear interpolation of a continuous random field on a d-dimensional cube. The approximation performance is measured by the integrated mean square error. Multivariate piecewise linear interpolator is…

We introduce a framework for robust uncertainty quantification in situations where labeled training data are corrupted, through noisy or missing labels. We build on conformal prediction, a statistical tool for generating prediction sets…

Suppose that a sequence of data points follows a distribution of a certain parametric form, but that one or more of the underlying parameters may change over time. This paper addresses various natural questions in such a framework. We…

Testing copula hypothesis is of fundamental importance in the applications of copula theory. In this paper we proposed a copula hypothesis testing with copula entropy. Since copula entropy is a unified theory in probability and therefore…

Detecting dependence between two random variables is a fundamental problem. Although the Pearson correlation is effective for capturing linear dependency, it can be entirely powerless for detecting nonlinear and/or heteroscedastic patterns.…

We propose discrete random-field models that are based on random partitions of $\mathbb{N}^2$. The covariance structure of each random field is determined by the underlying random partition. Functional central limit theorems are established…

We describe the limit (for two topologies) of large uniform random square permutations, i.e., permutations where every point is a record. The starting point for all our results is a sampling procedure for asymptotically uniform square…

Reproducibility is essential to reliable scientific discovery in high-throughput experiments. In this work we propose a unified approach to measure the reproducibility of findings identified from replicate experiments and identify putative…

Weighted histograms in Monte Carlo simulations are often used for the estimation of probability density functions. They are obtained as a result of random experiments with random events that have weights. In this paper, the bin contents of…

In this paper, we proposed a multivariate normality test based on copula entropy. The test statistic is defined as the difference between the copula entropies of unknown distribution and the Gaussian distribution with same covariances. The…

Motivated by problems on Brownian motion, we introduce a recursive scheme for a basis construction in the Hilbert space L^2(0,1) which is analogous to that of Haar and Walsh. More generally, we find a new decomposition theory for the…

The Brownian motion of a charged test particle caused by quantum electromagnetic vacuum fluctuations between two perfectly conducting plates is examined and the mean squared fluctuations in the velocity and position of the test particle are…

We study the upper and lower regularity dimensions in relation to the notions of doubling and uniformly perfect. These two regularity properties are closely related which is quantified thanks to the regularity dimensions. The regularity…

Analogues of the frequentist chi-square and F tests are proposed for testing goodness-of-fit and consistency for Bayesian models. Simple examples exhibit these tests' detection of inconsistency between consecutive experiments with identical…

We obtain a complete description for a probability measure to be doubling on an arbitrarily given uniform Cantor set. The question of which doubling measures on such a Cantor set can be extended to a doubling measure on [0; 1] is also…

This paper describes the quality of convergence to an infinitely divisible law relative to free multiplicative convolution. We show that convergence in distribution for products of identically distributed and infinitesimal free random…

In this work, we present a complete characterization of the covariance structure of number statistics in boxes for hyperuniform point processes. Under a standard integrability assumption, the covariance depends solely on the overlap of the…

Hyperuniformity characterizes a state of matter for which density fluctuations diminish towards zero at the largest length scales. However, the task of determining whether or not an experimental system is hyperuniform is experimentally…

We consider the basic statistical problem of detecting truncation of the uniform distribution on the Boolean hypercube by juntas. More concretely, we give upper and lower bounds on the problem of distinguishing between i.i.d. sample access…

Hyperuniformity is the study of stationary point processes with a sub-Poisson variance in a large window. In other words, counting the points of a hyperuniform point process that fall in a given large region yields a small-variance Monte…