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Many testing problems are readily amenable to randomised tests such as those employing data splitting. However despite their usefulness in principle, randomised tests have obvious drawbacks. Firstly, two analyses of the same dataset may…
Latent variable models are well-known to suffer from rank deficiencies, causing problems with convergence and stability. Such problems are compounded in the "reduced-group split-ballot multitrait-multimethod model", which omits a set of…
This paper considers the use of recently proposed optimal transport-based multivariate test statistics, namely rank energy and its variant the soft rank energy derived from entropically regularized optimal transport, for the unsupervised…
The sign and the signed-rank tests for univariate data are perhaps the most popular nonparametric competitors of the t test for paired sample problems. These tests have been extended in various ways for multivariate data in finite…
Increased attention has been given recently to the statistical analysis of variables with values on nonlinear manifolds. A natural but nontrivial problem in that context is the definition of quantile concepts. We are proposing a solution…
Permutation tests enable testing statistical hypotheses in situations when the distribution of the test statistic is complicated or not available. In some situations, the test statistic under investigation is multivariate, with the multiple…
We develop a new rank-based approach for univariate two-sample testing in the presence of missing data which makes no assumptions about the missingness mechanism. This approach is a theoretical extension of the Wilcoxon-Mann-Whitney test…
The framework of optimal transport has been leveraged to extend the notion of rank to the multivariate setting while preserving desirable properties of the resulting goodness-of-fit (GoF) statistics. In particular, the rank energy (RE) and…
Non-Euclidean data become more prevalent in practice, necessitating the development of a framework for statistical inference analogous to that for Euclidean data. Quantile is one of the most important concepts in traditional statistical…
A common method for deriving non-parametric tests is to reformulate a parametric test in terms of sample ranks. Despite being distribution free (even in finite samples), the resulting tests often display remarkable asymptotic power…
A number of applications require two-sample testing on ranked preference data. For instance, in crowdsourcing, there is a long-standing question of whether pairwise comparison data provided by people is distributed similar to…
For testing two random vectors for independence, we consider testing whether the distance of one vector from a center point is independent from the distance of the other vector from a center point by a univariate test. In this paper we…
How should researchers analyze randomized experiments in which the main outcome is latent and measured in multiple ways but each measure contains some degree of error? We first identify a critical study-specific noncomparability problem in…
This paper deals with testing the equality of $k$ ($k\ge 2$) distribution functions against possible stochastic ordering among them. Two classes of rank tests are proposed for this testing problem. The statistics of the tests under study…
Ranking populations such as institutions based on certain characteristics is often of interest, and these ranks are typically estimated using samples drawn from the populations. Due to sample randomness, it is important to quantify the…
We treat the problem of testing independence between m continuous variables when m can be larger than the available sample size n. We consider three types of test statistics that are constructed as sums or sums of squares of pairwise rank…
We consider the problem of testing the equality of conditional distributions of a response variable given a vector of covariates between two populations. Such a hypothesis testing problem can be motivated from various machine learning and…
We propose confidence regions for the parameters of incomplete models with exact coverage of the true parameter in finite samples. Our confidence region inverts a test, which generalizes Monte Carlo tests to incomplete models. The test…
Stochastic dominance is an important concept in probability theory, econometrics and social choice theory for robustly modeling agents' preferences between random outcomes. While many works have been dedicated to the univariate case, little…
Nonparametric tests for functional data are a challenging class of tests to work with because of the potentially high dimensional nature of the data. One of the main challenges for considering rank-based tests, like the Mann-Whitney or…