Related papers: A two-sample test for symmetric positive definite …
In this paper, we consider the nonparametric estimation of the multivariate probability density function and its partial derivative with a support on $[0,\infty)$. To this end we use the class of kernel estimators with asymmetric gamma…
Considering two independent Poisson processes, we address the question of testing equality of their respective intensities. We first propose single tests whose test statistics are U-statistics based on general kernel functions. The…
The log-normal distribution is one of the most common distributions used for modeling skewed and positive data. It frequently arises in many disciplines of science, specially in the biological and medical sciences. The statistical analysis…
We study the behavior of a real $p$-dimensional Wishart random matrix with $n$ degrees of freedom when $n,p\rightarrow\infty$ but $p/n\rightarrow 0$. We establish the existence of phase transitions when $p$ grows at the order…
Nonparametric estimation of copula density functions using kernel estimators presents significant challenges. One issue is the potential unboundedness of certain copula density functions at the corners of the unit square. Another is the…
In this paper we derive some new and practical results on testing and interval estimation problems for the population eigenvalues of a Wishart matrix based on the asymptotic theory for block-wise infinite dispersion of the population…
In this work, we consider the weighted difference of two independent complex Wishart matrices and derive the joint probability density function of the corresponding eigenvalues in a finite-dimension scenario using two distinct approaches.…
Random matrix theory has become a cornerstone in modern statistics and data science, providing fundamental tools for understanding high-dimensional covariance structures. Within this framework, the Wishart matrix plays a central role in…
Kernel methods provide a flexible and powerful framework for nonparametric statistical testing by embedding probability distributions into a reproducing kernel Hilbert space (RKHS). In this work, we study the kernel two-sample testing…
This paper considers the problem of testing the equality of two unspecified distributions. The classical omnibus tests such as the Kolmogorov-Smirnov and Cram\`er-von Mises are known to suffer from low power against essentially all but…
We consider the complex eigenvalues of a Wishart type random matrix model $X=X_1 X_2^*$, where two rectangular complex Ginibre matrices $X_{1,2}$ of size $N\times (N+\nu)$ are correlated through a non-Hermiticity parameter $\tau\in[0,1]$.…
A two-class mixture model, where the density of one of the components is known, is considered. We address the issue of the nonparametric adaptive estimation of the unknown probability density of the second component. We propose a randomly…
Recent work introduced deep kernel processes as an entirely kernel-based alternative to NNs (Aitchison et al. 2020). Deep kernel processes flexibly learn good top-layer representations by alternately sampling the kernel from a distribution…
We propose a framework to construct practical kernel-based two-sample tests from the family of $f$-divergences. The test statistic is computed from the witness function of a regularized variational representation of the divergence, which we…
We propose a two-sample testing procedure based on learned deep neural network representations. To this end, we define two test statistics that perform an asymptotic location test on data samples mapped onto a hidden layer. The tests are…
This paper addresses the multiple two-sample test problem in a graph-structured setting, which is a common scenario in fields such as Spatial Statistics and Neuroscience. Each node $v$ in fixed graph deals with a two-sample testing problem…
This article inspects whether a multivariate distribution is different from a specified distribution or not, and it also tests the equality of two multivariate distributions. In the course of this study, a graphical tool-kit using…
We propose the density ratio permutation test, a hypothesis test that assesses whether the ratio between two densities is proportional to a known function based on independent samples from each distribution. The test uses an efficient…
In this paper, we investigate the testing problem that the spectral density matrices of several, not necessarily independent, stationary processes are equal. Based on an $L_2$-type test statistic, we propose a new nonparametric approach,…
Are two sets of observations drawn from the same distribution? This problem is a two-sample test. Kernel methods lead to many appealing properties. Indeed state-of-the-art approaches use the $L^2$ distance between kernel-based distribution…