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We consider one of the most basic multiple testing problems that compares expectations of multivariate data among several groups. As a test statistic, a conventional (approximate) $t$-statistic is considered, and we determine its rejection…

Multi-label (ML) data deals with multiple classes associated with individual samples at the same time. This leads to the co-occurrence of several classes repeatedly, which indicates some existing correlation among them. In this article, the…

Classical analysis of variance requires that model terms be labeled as fixed or random and typically culminate by comparing variability from each batch (factor) to variability from errors; without a standard methodology to assess the…

We study the problem of multiple hypothesis testing for multidimensional data when inter-correlations are present. The problem of multiple comparisons is common in many applications. When the data is multivariate and correlated, existing…

Canonical correlation analysis (CCA) is a classic statistical method for discovering latent co-variation that underpins two or more observed random vectors. Several extensions and variations of CCA have been proposed that have strengthened…

In this paper, the defining properties of a valid measure of the dependence between two random variables are reviewed and complemented with two original ones, shown to be more fundamental than other usual postulates. While other popular…

In many scientific tasks we are interested in discovering whether there exist any correlations in our data. This raises many questions, such as how to reliably and interpretably measure correlation between a multivariate set of attributes,…

We develop factor copula models for analysing the dependence among mixed continuous and discrete responses. Factor copula models are canonical vine copulas that involve both observed and latent variables, hence they allow tail, asymmetric…

The objective of the present paper is to develop a minimax theory for the varying coefficient model in a non-asymptotic setting. We consider a high-dimensional sparse varying coefficient model where only few of the covariates are present…

This paper considers multiple regression procedures for analyzing the relationship between a response variable and a vector of covariates in a nonparametric setting where both tuning parameters and the number of covariates need to be…

Model averaging, as an appealing ensemble technique, strategically integrates all valuable information from candidate models to construct fast and accurate prediction. Despite of having been widely practiced in many fields such as…

Factor analysis is a flexible technique for assessment of multivariate dependence and codependence. Besides being an exploratory tool used to reduce the dimensionality of multivariate data, it allows estimation of common factors that often…

Model-free knockoffs is a recently proposed technique for identifying covariates that is likely to have an effect on a response variable. The method is an efficient method to control the false discovery rate in hypothesis tests for separate…

This paper considers inference for conditional moment inequality models using a multiscale statistic. We derive the asymptotic distribution of this test statistic and use the result to propose feasible critical values that have a simple…

Quantile regression is a powerful tool for detecting exposure-outcome associations given covariates across different parts of the outcome's distribution, but has two major limitations when the aim is to infer the effect of an exposure.…

Our purpose is to model the dependence between two random variables, taking into account a priori knowledge on these variables. For example, in many applications (oceanography, finance...), there exists an order relation between the two…

For many important problems the quantity of interest is an unknown function of the parameters, which is a random vector with known statistics. Since the dependence of the output on this random vector is unknown, the challenge is to identify…

Datasets containing both categorical and continuous variables are frequently encountered in many areas, and with the rapid development of modern measurement technologies, the dimensions of these variables can be very high. Despite the…

Nonparametric and nonlinear measures of statistical dependence between pairs of random variables are important tools in modern data analysis. In particular the emergence of large data sets can now support the relaxation of linearity…

Quantification, variously called "supervised prevalence estimation" or "learning to quantify", is the supervised learning task of generating predictors of the relative frequencies (a.k.a. "prevalence values") of the classes of interest in…