Related papers: Inference for Dispersion and Curvature of Random O…
For a general radially symmetric, non-increasing, non-negative kernel $h\in L ^ 1 _{loc} ( R ^ d)$, we study the rigidity of measurable sets in $R ^ d$ with constant nonlocal $h$-mean curvature. Under a suitable "improved integrability"…
Weighting methods are widely used to adjust for covariates in observational studies, sample surveys, and regression settings. In this paper, we study a class of recently proposed weighting methods which find the weights of minimum…
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…
Using a discrete wavelet based space-scale decomposition (SSD), the spectrum of the skewness and kurtosis is developed to describe the non-Gaussian signatures in cosmologically interesting samples. Because the basis of the discrete wavelet…
In this paper, the statistical properties of Newton s method algorithm output in a specific case have been studied. The relative frequency density of this sample converges to a well-defined function, prompting us to explore its…
We consider finite point subsets (distributions) in compact metric spaces. In the case of general rectifiable metric spaces, non-trivial bounds for sums of distances between points of distributions and for discrepancies of distributions in…
Application of the exact statistical inference frequently leads to a non-standard probability distributions of the considered estimators or test statistics. The exact distributions of many estimators and test statistics can be specified by…
We develop inference and testing procedures for conditional dispersion and skewness in a nonparametric regression setup based on statistical depth functions. The methods developed can be applied in situations, where the response is…
Dynamical systems with $\epsilon$ small random perturbations appear in both continuous mechanical motions and discrete stochastic chemical kinetics. The present work provides a detailed analysis of the central limit theorem (CLT), with a…
We study the singular limit of a spatially inhomogeneous and anisotropic reaction-diffusion equation. We use a Finsler metric related to the anisotropic diffusion term and work in relative geometry. We prove a weak comparison principle and…
Recent theoretical works have characterized the dynamics of wide shallow neural networks trained via gradient descent in an asymptotic mean-field limit when the width tends towards infinity. At initialization, the random sampling of the…
In order to improve the advantages and the reliability of the second derivative method in tracking the position of extrema from experimental curves, we develop a novel analysis method based on the mathematical concept of curvature. We…
Our proper acceleration with respect to the Cosmic Microwave Background results in a real-time change of the angular position of distant extragalactic sources. The cosmological component of this aberration drift signal, the non-inertial…
Modern longitudinal data, for example from wearable devices, measures biological signals on a fixed set of participants at a diverging number of time points. Traditional statistical methods are not equipped to handle the computational…
One of the main problems of observational cosmology is to determine the range in which a reliable measurement of galaxy correlations is possible. This corresponds to determine the shape of the correlation function, its possible evolution…
Several new geometric quantile-based measures for multivariate dispersion, skewness, kurtosis, and spherical asymmetry are defined. These measures differ from existing measures, which use volumes and are easy to calculate. Some theoretical…
This paper considers inference for conditional moment inequality models using a multiscale statistic. We derive the asymptotic distribution of this test statistic and use the result to propose feasible critical values that have a simple…
We study time series concerning rare events. The occurrence of a rare event is depicted as a jump of constant intensity always occurring in the same direction, thereby generating an asymmetric diffusion process. We consider the case where…
Chatteerjee and Diaconis have recently shown the asymptotic normality for the joint distribution of the number of descents and inverse descents in a random permutation. A noteworthy point of their results is that the asymptotic variance of…
We provide a distribution-free test that can be used to determine whether any two joint distributions $p$ and $q$ are statistically different by inspection of a large enough set of samples. Following recent efforts from Long et al. [1], we…