Related papers: Testing multivariate normality by zeros of the har…
In this paper, we develop a simple non-parametric test for testing normal distribution based on the distance between empirical zero-bias transformation and empirical distribution. The asymptotic properties of the test statistic are studied.…
While attractive from a theoretical perspective, finely stratified experiments such as paired designs suffer from certain analytical limitations not present in block-randomized experiments with multiple treated and control individuals in…
We derive the limit null distribution of the class of Sobolev tests of uniformity on the hypersphere when the dimension and the sample size diverge to infinity at arbitrary rates. The limiting non-null behavior of these tests is obtained…
An approach to solve the critical problem of testing quantum effects of spatial noncommutativity is proposed. Magnetic hyperfine structures in a Rydberg system induced by fractional angular momentum originated from spatial noncommutativity…
We propose a family of tests of the validity of the assumptions underlying independent component analysis methods. The tests are formulated as L2-type procedures based on characteristic functions and involve weights; a proper choice of…
We study (asymmetric) $U$-statistics based on a stationary sequence of $m$-dependent variables; moreover, we consider constrained $U$-statistics, where the defining multiple sum only includes terms satisfying some restrictions on the gaps…
Starting from the semi-classical spectrum of Schr\"odinger operators $-h^2\Delta+V$ (on $\mathbb{R}^n$ or on a Riemannian manifold) it is possible to detect critical levels of the potential $V$. Via micro-local methods one can express…
We study the existence, strong consistency and asymptotic normality of estimators obtained from estimating functions, that are p-dimensional martingale transforms. The problem is motivated by the analysis of evolutionary clustered data,…
We consider nonlinear Schrodinger equations with either local or nonlocal nonlinearities. In addition, we include periodic potentials as used, for example, in matter wave experiments in optical lattices. By considering the corresponding…
We study the Cauchy problem for Schr\"odinger type stochastic partial differential equations with uniformly bounded coefficients on a curved space. We give conditions on the coefficients, on the drift and diffusion terms, on the Cauchy…
We consider a derivative nonlinear Schr\"odinger equation with a general nonlinearity. This equation has a two parameter family of solitary wave solutions. We prove orbital stability/instability results that depend on the strength of the…
We study Dorfman's classical group testing protocol in a novel setting where individual specimen statuses are modeled as exchangeable random variables. We are motivated by infectious disease screening. In that case, specimens which arrive…
We report on the possibilities of using the method of normal fundamental systems for solving some problems of oscillation theory. Large elastic dynamical systems with continuous and discrete parameters are considered, which have many…
In statistical analysis, measuring a score of predictive performance is an important task. In many scientific fields, appropriate scores were tailored to tackle the problems at hand. A proper score is a popular tool to obtain statistically…
Although several nonparametric tests are available for testing population identical distributions or equal means in multiple groups problem, the Van der Waerden test has asymptotically the same efficiency as the classical one-way analysis…
We continue the analysis of random series associated to the multidimensional harmonic oscillator $-\Delta + |x|^2$ on $\mathbb{R}^d$ with d \geq 2$$. More precisely we obtain a necessary and sufficient condition to get the almost sure…
Consider a random sample of $n$ independently and identically distributed $p$-dimensional normal random vectors. A test statistic for complete independence of high-dimensional normal distributions, proposed by Schott (2005), is defined as…
We present simple, self-contained proofs of correctness for algorithms for linearity testing and program checking of linear functions on finite subsets of integers represented as n-bit numbers. In addition we explore a generalization of…
In this paper we consider testing the equality of probability vectors of two independent multinomial distributions in high dimension. The classical chi-square test may have some drawbacks in this case since many of cell counts may be zero…
This paper proposes a new test for inequalities that are linear in possibly partially identified nuisance parameters. This type of hypothesis arises in a broad set of problems, including subvector inference for linear unconditional moment…