Related papers: Single-Observation Uniformity Testing under Increa…
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 scientific inference problems, the underlying statistical modeling assumptions have a crucial impact on the end results. There exist, however, only a few automatic means for validating these fundamental modelling assumptions. The…
Teramoto et al. defined a new measure called the gap ratio that measures the uniformity of a finite point set sampled from $\cal S$, a bounded subset of $\mathbb{R}^2$. We generalize this definition of measure over all metric spaces by…
We propose a novel approach to uniformity testing on the $d$-dimensional unit hypersphere $\mathcal{S}^{d-1}$ based on maximal projections. This approach gives a unifying view on the classical uniformity tests of Rayleigh and Bingham, and…
In this work we study the possibility of detecting the so-called strong stochasticity threshold, i.e. the transition between weak and strong chaos as the energy density of the system is increased, in anharmonic oscillator chains by means of…
It has recently been shown that there are substantial differences in the regularity behavior of the empirical process based on scalar diffusions as compared to the classical empirical process, due to the existence of diffusion local time.…
We propose a goodness-of-fit test for degree-corrected stochastic block models (DCSBM). The test is based on an adjusted chi-square statistic for measuring equality of means among groups of $n$ multinomial distributions with $d_1,\dots,d_n$…
The density matrix in quantum mechanics parameterizes the statistical properties of the system under observation, just like a classical probability distribution does for classical systems. The expectation value of observables cannot be…
We develop a uniform inference theory for high-dimensional slope parameters in threshold regression models, allowing for either cross-sectional or time series data. We first establish oracle inequalities for prediction errors, and L1…
For a certain parametrized family of maps on the circle, with critical points and logarithmic singularities where derivatives blow up to infinity, a positive measure set of parameters was constructed in [19], corresponding to maps which…
We show that the recently discovered quantum-enhanced measurement protocol of coherent averaging that is capable of achieving Heisenberg-limited sensitivity without using entanglement, has a classical analogue. The classical protocol uses N…
We introduce a new notion of a harmonic measure for a $d$-dimensional set in $\R^n$ with $d<n-1$, that is, when the codimension is strictly bigger than 1. Our measure is associated to a degenerate elliptic PDE, it gives rise to a…
Recent advances in quantized compressed sensing and high-dimensional estimation have shown that signal recovery is even feasible under strong non-linear distortions in the observation process. An important characteristic of associated…
A test of the null hypothesis that a hazard rate is monotone nondecreasing, versus the alternative that it is not, is proposed. Both the test statistic and the means of calibrating it are new. Unlike previous approaches, neither is based on…
In astronomy, there is an opportunity to enhance the practice of validating models through statistical techniques, specifically to account for measurement error uncertainties. While models are commonly used to describe observations, there…
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.…
We study the variance in the number of points contained within a window $\Omega$ of arbitrary size, and to further illuminate our understanding of {\it hyperuniform} systems, i.e., point patterns that do not possess long-wavelength…
In the uniformity testing task, an algorithm is provided with samples from an unknown probability distribution over a (known) finite domain, and must decide whether it is the uniform distribution, or, alternatively, if its total variation…
On the basis of a model system of pillars built of unit cubes, a two-component entropic measure for the multiscale analysis of spatio-compositional inhomogeneity is proposed. It quantifies the statistical dissimilarity per cell of the…
Measurement non-invariance arises when the psychometric properties of a scale differ across subgroups, undermining the validity of group comparisons. At the item level, such non-invariance manifests as differential item functioning (DIF),…