Related papers: Testing the simplifying assumption in high-dimensi…

Regular vine sequences permit the organisation of variables in a random vector along a sequence of trees. Regular vine models have become greatly popular in dependence modelling as a way to combine arbitrary bivariate copulas into…

While powerful methods have been developed for high-dimensional hypothesis testing assuming orthogonal parameters, current approaches struggle to generalize to the more common non-orthogonal case. We propose Stable Distillation (SD), a…

This paper aims to develop an effective model-free inference procedure for high-dimensional data. We first reformulate the hypothesis testing problem via sufficient dimension reduction framework. With the aid of new reformulation, we…

High-dimensional changepoint inference that adapts to various change patterns has received much attention recently. We propose a simple, fast yet effective approach for adaptive changepoint testing. The key observation is that two…

The structural information in high-dimensional transposable data allows us to write the data recorded for each subject in a matrix such that both the rows and the columns correspond to variables of interest. One important problem is to test…

Understanding statistical inference under possibly non-sparse high-dimensional models has gained much interest recently. For a given component of the regression coefficient, we show that the difficulty of the problem depends on the sparsity…

Inference of the conditional dependence structure is challenging when many covariates are present. In numerous applications, only a low-dimensional projection of the covariates influences the conditional distribution. The smallest subspace…

Standard penalized methods of variable selection and parameter estimation rely on the magnitude of coefficient estimates to decide which variables to include in the final model. However, coefficient estimates are unreliable when the design…

In this paper, we consider the problem of testing properties of joint distributions under the Conditional Sampling framework. In the standard sampling model, the sample complexity of testing properties of joint distributions is exponential…

Multivariate Gaussian distributions enjoy Gaussian conditional distributions that makes conditioning easy: conditioning boils down to implementing analytical formulae for conditional means and covariances. For more general distributions,…

Systems subject to uncertain inputs produce uncertain responses. Uncertainty quantification (UQ) deals with the estimation of statistics of the system response, given a computational model of the system and a probabilistic model of its…

Testing for pairwise independence for the case where the number of variables may be of the same size or even larger than the sample size has received increasing attention in the recent years. We contribute to this branch of the literature…

The paper considers variable selection in linear regression models where the number of covariates is possibly much larger than the number of observations. High dimensionality of the data brings in many complications, such as (possibly…

This study suggests a coupling uncertainty analysis method to investigate the stiffness characteristics of variable stiffness (VS) composite. The D-vine copula function is used to address the coupling of random variables. To identify the…

Current statistical inference problems in areas like astronomy, genomics, and marketing routinely involve the simultaneous testing of thousands -- even millions -- of null hypotheses. For high-dimensional multivariate distributions, these…

Curse of Dimensionality is an unavoidable challenge in statistical probability models, yet diffusion models seem to overcome this limitation, achieving impressive results in high-dimensional data generation. Diffusion models assume that…

Test of independence is of fundamental importance in modern data analysis, with broad applications in variable selection, graphical models, and causal inference. When the data is high dimensional and the potential dependence signal is…

We propose a two-sample test for high-dimensional means that requires neither distributional nor correlational assumptions, besides some weak conditions on the moments and tail properties of the elements in the random vectors. This…

The statistical analysis of univariate quantiles is a well developed research topic. However, there is a need for research in multivariate quantiles. We construct bivariate (conditional) quantiles using the level curves of vine copula based…

So called pair copula constructions (PCCs), specifying multivariate distributions only in terms of bivariate building blocks (pair copulas), constitute a flexible class of dependence models. To keep them tractable for inference and model…