Related papers: Sequential block bootstrap in a Hilbert space with…
We propose a flexible and robust nonparametric framework for testing spatial dependence in two- and three-dimensional random fields. Our approach involves converting spatial data into one-dimensional time series using space-filling Hilbert…
An algorithm is described that enables efficient deterministic approximate computation of the bootstrap distribution for any linear bootstrap method $T_n^*$, alleviating the need for repeated resampling from observations (resp.…
Hypothesis testing for the slope function in functional linear regression is of both practical and theoretical interest. We develop a novel test for the nullity of the slope function, where testing the slope function is transformed into…
This paper presents new results on Functional Analysis of Variance for fixed effect models with correlated Hilbert-valued Gaussian error components. The geometry of the Reproducing Kernel Hilbert Space (RKHS) of the error term is considered…
We investigate consequences of allowing the Hilbert space of a quantum system to have a time-dependent metric. For a given possibly nonstationary quantum system, we show that the requirement of having a unitary Schreodinger time-evolution…
Three-dimensional theories with cubic symmetry are studied using the machinery of the numerical conformal bootstrap. Crossing symmetry and unitarity are imposed on a set of mixed correlators, and various aspects of the parameter space are…
The rise in complexity of network data in neuroscience, social networks, and protein-protein interaction networks has been accompanied by several efforts to model and understand these data at different scales. A key multiscale network…
In this paper, two tests, based on CUSUM of the residuals and least squares estimation, are studied to detect in real time a change-point in a nonlinear model. A first test statistic is proposed by extension of a method already used in the…
Motivated by statistical inference problems in high-dimensional time series data analysis, we first derive non-asymptotic error bounds for Gaussian approximations of sums of high-dimensional dependent random vectors on hyper-rectangles,…
We work out all of the details required for implementation of the conformal bootstrap program applied to the four-point function of two scalars and two vectors in an abstract conformal field theory in arbitrary dimension. This includes a…
The numerical conformal bootstrap is used to study mixed correlators in $\mathcal{N}=1$ superconformal field theories (SCFTs) in $d=4$ spacetime dimensions. Systems of four-point functions involving scalar chiral and real operators are…
Functional panels are collections of functional time series, and arise often in the study of high frequency multivariate data. We develop a portmanteau style test to determine if the cross-sections of such a panel are independent and…
Generative models based on invertible transformations provide a physics-aware route to sample equilibrium configurations directly from the Boltzmann distribution, enabling efficient exploration of complex thermodynamic landscapes. Here, we…
We propose a novel approach for estimating the location of block boundaries (change-points) in a random matrix consisting of a block wise constant matrix observed in white noise. Our method consists in rephrasing this task as a variable…
Persistent homology, while ostensibly measuring changes in topology, captures multiscale geometrical information. It is a natural tool for the analysis of point patterns. In this paper we explore the statistical power of the (persistent…
Usually, the dynamics of linear time-invariant systems described by an integral operator of convolution type, which is defined in the Hilbert space of Lebesgue square integrable functions on the whole line. Such a description leads to…
In this paper we investigate how the bootstrap can be applied to time series regressions when the volatility of the innovations is random and non-stationary. The volatility of many economic and financial time series displays persistent…
Eficient, physically-inspired descriptors of the structure and composition of molecules and materials play a key role in the application of machine-learning techniques to atomistic simulations. The proliferation of approaches, as well as…
We introduce a methodology to test models with spatial variations of the fine-structure constant $\alpha$, based on the calculation of the angular power spectrum of these measurements. This methodology enables comparisons of observations…
Contraction theory for dynamical systems on Euclidean spaces is well-established. For contractive (resp. semi-contractive) systems, the distance (resp. semi-distance) between any two trajectories decreases exponentially fast. For partially…