Related papers: Multivariate Ranks and Quantiles using Optimal Tra…
In this paper we propose and study a class of nonparametric, yet interpretable measures of association between two random vectors $X$ and $Y$ taking values in $\mathbb{R}^{d_1}$ and $\mathbb{R}^{d_2}$ respectively ($d_1, d_2\ge 1$). These…
The Glivenko--Cantelli theorem is a uniform version of the strong law of large numbers. It states that for every IID sequence of random variables, the empirical measure converges to the underlying distribution (in the sense of uniform…
We are deriving optimal rank-based tests for the adequacy of a vector autoregressive-moving average (VARMA) model with elliptically contoured innovation density. These tests are based on the ranks of pseudo-Mahalanobis distances and on…
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…
The sign test (Arbuthnott, 1710) and the Wilcoxon signed-rank test (Wilcoxon, 1945) are among the first examples of a nonparametric test. These procedures -- based on signs, (absolute) ranks and signed-ranks -- yield distribution-free tests…
The large-sample behavior of non-degenerate multivariate $U$-statistics of arbitrary degree is investigated under the assumption that their kernel depends on parameters that can be estimated consistently. Mild regularity conditions are…
We derive limit distributions for certain empirical regularized optimal transport distances between probability distributions supported on a finite metric space and show consistency of the (naive) bootstrap. In particular, we prove that the…
We propose a framework for conditional vector quantile regression (CVQR) that combines neural optimal transport with amortized optimization, and apply it to multivariate conformal prediction. Classical quantile regression does not extend…
Optimal transport maps define a one-to-one correspondence between probability distributions, and as such have grown popular for machine learning applications. However, these maps are generally defined on empirical observations and cannot be…
We believe three ingredients are needed for further progress in persistence and its use: invariants not relying on decomposition theorems to go beyond 1-dimension, outcomes suitable for statistical analysis and a setup adopted for…
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…
In this paper, I propose a general algorithm for multiple change point analysis via multivariate distribution-free nonparametric testing based on the concept of ranks that are defined by measure transportation. Multivariate ranks and the…
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…
The paper presents a systematic theory for asymptotic inference of autocovariances of stationary processes. We consider nonparametric tests for serial correlations based on the maximum (or ${\cal L}^\infty$) and the quadratic (or ${\cal…
We consider invariant transports of stationary random measures on $\mathbb{R}^d$ and establish natural mixing criteria that guarantee persistence of asymptotic variances. To check our mixing assumptions, which are based on two-point Palm…
The classical theory of rank-based inference is entirely based either on ordinary ranks, which do not allow for considering location (intercept) parameters, or on signed ranks, which require an assumption of symmetry. If the median, in the…
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…
In this paper, I propose a general procedure for multivariate distribution-free nonparametric testing derived from the concept of ranks that are based upon measure transportation in the context of multiple change point analysis. I will use…
We develop asymptotic theory for weighted likelihood estimators (WLE) under two-phase stratified sampling without replacement. We also consider several variants of WLEs involving estimated weights and calibration. A set of empirical process…
In this paper we propose and study a class of simple, nonparametric, yet interpretable measures of association between two random variables $X$ and $Y$ taking values in general topological spaces. These nonparametric measures -- defined…