Related papers: Brownian sheet and uniformity tests on the hypercu…
In this paper, we develop a general machinery for finding explicit uniform probability and moment bounds on sub-additive positive functionals of random processes. Using the developed general technique, we derive uniform bounds on the…
The assumption of separability is a simplifying and very popular assumption in the analysis of spatio-temporal or hypersurface data structures. It is often made in situations where the covariance structure cannot be easily estimated, for…
Distance correlation is a new class of multivariate dependence coefficients applicable to random vectors of arbitrary and not necessarily equal dimension. Distance covariance and distance correlation are analogous to product-moment…
We study robust estimators of the mean of a probability measure $P$, called robust empirical mean estimators. This elementary construction is then used to revisit a problem of aggregation and a problem of estimator selection, extending…
In this paper, we introduce a model of Brownian polymer in a continuous random environment. The asymptotic behavior of the partition function associated to this polymer measure is studied, and we are able to separate a weak and strong…
Summary: We describe a tool for quantifying the uniformity of mapped reads in high-throughput sequencing experiments. Our statistic directly measures the uniformity of both read position and fragment length, and we explain how to compute a…
The assumption of normality has underlain much of the development of statistics, including spatial statistics, and many tests have been proposed. In this work, we focus on the multivariate setting and first review the recent advances in…
We derive multiscale statistics for deconvolution in order to detect qualitative features of the unknown density. An important example covered within this framework is to test for local monotonicity on all scales simultaneously. We…
Bell tests are of profound statistical nature. Besides physical considerations, the proper understanding of their implications should involve detailed statistical analyses. In this regard, recent works have shown that their consequences and…
The interplay between Coulomb friction and random excitations is studied experimentally by means of a rotating probe in contact with a stationary granular gas. The granular material is independently fluidized by a vertical shaker, acting as…
Conformal testing is a way of testing the IID assumption based on conformal prediction. The topic of this note is computational evaluation of the performance of conformal testing in a model situation in which IID binary observations…
Cubical complexes are metric spaces constructed by gluing together unit cubes in an analogous way to the construction of simplicial complexes. We construct Brownian motion on such spaces, define random walks, and prove that the transition…
We describe a measurement device principle based on discrete iterations of Bayesian updating of system state probability distributions. Although purely classical by nature, these measurements are accompanied with a progressive collapse of…
We define weighted fractional Brownian sheets, which are a class of Gaussian random fields with four parameters that include fractional Brownian sheets as special cases, and we give some of their properties. We show that for certain values…
We propose a new test for the hypothesis that a bivariate copula is an Archimedean copula. The test statistic is based on a combination of two measures resulting from the characterization of Archimedean copulas by the property of…
Permutation tests date back nearly a century to Fisher's randomized experiments, and remain an immensely popular statistical tool, used for testing hypotheses of independence between variables and other common inferential questions. Much of…
The Bounded Negativity Conjecture predicts that for every complex projective surface $X$ there exists a number $b(X)$ such that $C^2\geq -b(X)$ holds for all reduced curves $C\subset X$. For birational surfaces $f:Y\to X$ there have been…
We propose a class of tests for linear regression on concomitants (induced order statistics). These tests are based on sequential sums of regression residuals. We self-center and self-normalize these sums. The resulting process is called an…
Robust model fitting is a fundamental problem in computer vision: used to pre-process raw data in the presence of outliers. Maximisation of Consensus (MaxCon) is one of the most popular robust criteria and widely used. Recently (Tennakoon…
After variable selection, standard inferential procedures for regression parameters may not be uniformly valid; there is no finite-sample size at which a standard test is guaranteed to approximately attain its nominal size. This problem is…