Related papers: Two-Sample Smooth Tests for the Equality of Distri…
This paper studies the goodness of fit test for the bivariate Hermite distribution. Specifically, we propose and study a Cram\'er-von Mises-type test based on the empirical probability generation function. The bootstrap can be used to…
Statistical depth, which measures the center-outward rank of a given sample with respect to its underlying distribution, has become a popular and powerful tool in nonparametric inference. In this paper, we investigate the use of statistical…
Testing for the equality of two high-dimensional distributions is a challenging problem, and this becomes even more challenging when the sample size is small. Over the last few decades, several graph-based two-sample tests have been…
The problem of testing equality of the entire second order structure of two independent functional linear processes is considered. A fully functional $L^2$-type test is developed which evaluates, over all frequencies, the Hilbert-Schmidt…
Nonparametric two-sample testing is a classical problem in inferential statistics. While modern two-sample tests, such as the edge count test and its variants, can handle multivariate and non-Euclidean data, contemporary gargantuan datasets…
Two-sample tests are important in statistics and machine learning, both as tools for scientific discovery as well as to detect distribution shifts. This led to the development of many sophisticated test procedures going beyond the standard…
Two-sample hypothesis testing-determining whether two sets of data are drawn from the same distribution-is a fundamental problem in statistics and machine learning with broad scientific applications. In the context of nonparametric testing,…
Goodness-of-fit tests are crucial tools for assessing the validity of statistical models. In this paper, we introduce a novel approach, the Spectral Smooth Test (SST), that generalizes Neyman's smooth test to high-dimensional data settings.…
We construct new testing procedures for spherical and elliptical symmetry based on the characterization that a random vector $X$ with finite mean has a spherical distribution if and only if $\Ex[u^\top X | v^\top X] = 0$ holds for any two…
In this paper, we propose a new test for the equality of several covariance functions for functional data. Its test statistic is taken as the supremum value of the sum of the squared differences between the estimated individual covariance…
A consistent goodness-of-fit test for distributional regression is introduced. The test statistic is based on a process that traces the difference between a nonparametric and a semi-parametric estimate of the marginal distribution function…
The two-sample test is a fundamental problem in statistics with a wide range of applications. In the realm of high-dimensional data, nonparametric methods have gained prominence due to their flexibility and minimal distributional…
The problem of comparing the entire second order structure of two functional processes is considered and a $L^2$-type statistic for testing equality of the corresponding spectral density operators is investigated. The test statistic…
Two-sample testing is a fundamental problem in statistics. Despite its long history, there has been renewed interest in this problem with the advent of high-dimensional and complex data. Specifically, in the machine learning literature,…
We propose optimal Bayesian two-sample tests for testing equality of high-dimensional mean vectors and covariance matrices between two populations. In many applications including genomics and medical imaging, it is natural to assume that…
The two-sample problem, which consists in testing whether independent samples on $\mathbb{R}^d$ are drawn from the same (unknown) distribution, finds applications in many areas. Its study in high-dimension is the subject of much attention,…
In this paper, we consider the problem of testing the equality of two multivariate distributions based on geometric graphs constructed using the interpoint distances between the observations. These include the tests based on the minimum…
Two new omnibus tests of uniformity for data on the hypersphere are proposed. The new test statistics exploit closed-form expressions for orthogonal polynomials, feature tuning parameters, and are related to a "smooth maximum" function and…
Test statistics which are invariant under various subgroups of the orthogonal group are shown to provide tests whose powers are asymptotically equal to their level against the usual type of contiguous alternative in models where the number…
In this article, we present a nonparametric method for the general two-sample problem involving functional random variables modelled as elements of a separable Hilbert space ${\cal H}$. First, we present a general recipe based on linear…