Related papers: On the Finite-Sample Performance of Measure Transp…
For a probability P in $R^d$ its center outward distribution function $F_{\pm}$, introduced in Chernozhukov et al. (2017) and Hallin et al. (2021), is a new and successful concept of multivariate distribution function based on mass…
Optimization problems with rank constraints arise in many applications, including matrix regression, structured PCA, matrix completion and matrix decomposition problems. An attractive heuristic for solving such problems is to factorize the…
A popular approach for testing if two univariate random variables are statistically independent consists of partitioning the sample space into bins, and evaluating a test statistic on the binned data. The partition size matters, and the…
In the context of high-dimensional data, we investigate the one-sample location testing problem. We introduce a max-type test based on the weighted spatial sign, which exhibits exceptional performance, particularly in the presence of sparse…
We propose new concepts of statistical depth, multivariate quantiles, ranks and signs, based on canonical transportation maps between a distribution of interest on $R^d$ and a reference distribution on the $d$-dimensional unit ball. The new…
In many real-world prediction tasks, class labels contain information about the relative order between labels that are not captured by commonly used loss functions such as multicategory cross-entropy. Recently, the preference for unimodal…
We address the issue of semiparametric efficiency in the bivariate regression problem with a highly persistent predictor, where the joint distribution of the innovations is regarded an infinite-dimensional nuisance parameter. Using a…
We propose and analyse a reduced-rank method for solving least-squares regression problems with infinite dimensional output. We derive learning bounds for our method, and study under which setting statistical performance is improved in…
Sample size calculations can be challenging with skewed continuous outcomes in randomized controlled trials (RCTs). Standard t-test-based calculations may require data transformation, which may be difficult before data collection.…
Determining the precise rank is an important problem in many large-scale applications with matrix data exploiting low-rank plus noise models. In this paper, we suggest a universal approach to rank inference via residual subsampling (RIRS)…
Machine-learning classifiers can be leveraged as a two-sample statistical test. Suppose each sample is assigned a different label and that a classifier can obtain a better-than-chance result discriminating them. In this case, we can infer…
Continuity of the value of the martingale optimal transport problem on the real line w.r.t. its marginals was recently established in Backhoff-Veraguas and Pammer [2] and Wiesel [21]. We present a new perspective of this result using the…
Conformal prediction has been a very popular method of distribution-free predictive inference in recent years in machine learning and statistics. Its popularity stems from the fact that it works as a wrapper around any prediction algorithm…
Testing for independence between two random vectors is a fundamental problem in statistics. It is observed from empirical studies that many existing omnibus consistent tests may not work well for some strongly nonmonotonic and nonlinear…
Scholars frequently use covariate balance tests to test the validity of natural experiments and related designs. Unfortunately, when measured covariates are unrelated to potential outcomes, balance is uninformative about key identification…
High-dimensional data sets are commonly collected in many contemporary applications arising in various fields of scientific research. We present two views of finite samples in high dimensions: a probabilistic one and a nonprobabilistic one.…
A new class of general exponential ranking models is introduced which we label angle-based models for ranking data. A consensus score vector is assumed, which assigns scores to a set of items, where the scores reflect a consensus view of…
This paper introduces a novel framework for distributed two-sample testing using the Integrated Transportation Distance (ITD), an extension of the Optimal Transport distance. The approach addresses the challenges of detecting distributional…
We collect in this note some observations on the role of symmetries in Bayesian inference problems, that can be useful or detrimental depending on the way they act on the signal and on the observations. We emphasize in particular the need…
We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…