Related papers: On structure testing for component covariance matr…
This paper investigates a statistical procedure for testing the equality of two independent estimated covariance matrices when the number of potentially dependent data vectors is large and proportional to the size of the vectors, that is,…
In this paper, we establish the central limit theorem (CLT) for linear spectral statistics (LSSs) of a large-dimensional sample covariance matrix when the population covariance matrices are involved with diverging spikes. This constitutes a…
In this paper we consider some hypothesis tests within a family of Wishart distributions, where both the sample space and the parameter space are symmetric cones. For such testing problems, we first derive the joint density of the ordered…
This paper introduces two new families of non-parametric tests of goodness-of-fit on the compact classical groups. One of them is a family of tests for the eigenvalue distribution induced by the uniform distribution, which is consistent…
In this paper, we give an explanation to the failure of two likelihood ratio procedures for testing about covariance matrices from Gaussian populations when the dimension is large compared to the sample size. Next, using recent central…
Spontaneous collapse models aim at solving the measurement problem of quantum mechanics by introducing collapse of wave function as an ontologically objective mechanism that suppresses macroscopic superpositions. In particular, the strength…
In this self-contained chapter, we revisit a fundamental problem of multivariate statistics: estimating covariance matrices from finitely many independent samples. Based on massive Multiple-Input Multiple-Output (MIMO) systems we illustrate…
Time in-homogeneous cyclic Markov chain Monte Carlo (MCMC) samplers, including deterministic scan Gibbs samplers and Metropolis within Gibbs samplers, are extensively used for sampling from multi-dimensional distributions. We establish a…
Recent measurements of the Gottfried sum rule have focused attention on the possibility of substantial flavor symmetry breaking in the proton sea. This is confirmed by pp and pD Drell-Yan processes measured at FNAL. Theoretical models used…
We examine the possibility that the form of the lepton mixing matrix can be determined by extremising the Jarlskog flavour invariants associated, eg. with the commutator ($C$) of the lepton mass matrices. Introducing a strictly covariant…
We consider the problem of estimating a high-dimensional covariance matrix from a small number of observations when covariates on pairs of variables are available and the variables can have spatial structure. This is motivated by the…
In this paper, our objective is to present a constraining principle governing the spectral properties of the sample covariance matrix. This principle exhibits harmonious behavior across diverse limiting frameworks, eliminating the need for…
We consider the problem of closeness testing for two discrete distributions in the practically relevant setting of \emph{unequal} sized samples drawn from each of them. Specifically, given a target error parameter $\varepsilon > 0$, $m_1$…
This paper aims to test the number of spikes in a generalized spiked covariance matrix, the spiked eigenvalues of which may be extremely larger or smaller than the non-spiked ones. For a high-dimensional problem, we first propose a general…
Quantum Clustering is a powerful method to detect clusters in data with mixed density. However, it is very sensitive to a length parameter that is inherent to the Schr\"odinger equation. In addition, linking data points into clusters…
Recently, Brand, Ganian and Simonov introduced a parameterized refinement of the classical PAC-learning sample complexity framework. A crucial outcome of their investigation is that for a very wide range of learning problems, there is a…
For high-dimensional small sample size data, Hotelling's T2 test is not applicable for testing mean vectors due to the singularity problem in the sample covariance matrix. To overcome the problem, there are three main approaches in the…
We investigate whether the Wigner semi-circle and Marcenko-Pastur distributions, often used for deep neural network theoretical analysis, match empirically observed spectral densities. We find that even allowing for outliers, the observed…
We propose a phenomenological model of lepton mixing and CP violation based on the flavor democracy of charge leptons and the mass degeneracy of neutrinos. A nearly bi-maximal flavor mixing pattern, which is favored by current data on…
Dimension reduction for high-dimensional compositional data plays an important role in many fields, where the principal component analysis of the basis covariance matrix is of scientific interest. In practice, however, the basis variables…