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While there exists several inferential methods for analyzing functional data in factorial designs, there is a lack of statistical tests that are valid (i) in general designs, (ii) under non-restrictive assumptions on the data generating…

Constraint-based causal discovery algorithms utilize many statistical tests for conditional independence to uncover networks of causal dependencies. These approaches to causal discovery rely on an assumed correspondence between the…

Multivariate time series data that capture the temporal evolution of interconnected systems are ubiquitous in diverse areas. Understanding the complex relationships and potential dependencies among co-observed variables is crucial for the…

Diagnostic accuracy studies assess sensitivity and specificity of a new index test in relation to an established comparator or the reference standard. The development and selection of the index test is usually assumed to be conducted prior…

Multimodal data, where different types of data are collected from the same subjects, are fast emerging in a large variety of scientific applications. Factor analysis is commonly used in integrative analysis of multimodal data, and is…

High-dimensional vector autoregression with measurement error is frequently encountered in a large variety of scientific and business applications. In this article, we study statistical inference of the transition matrix under this model.…

The problem of identifying regions of spatially interesting, different or adversarial behavior is inherent to many practical applications involving distributed multisensor systems. In this work, we develop a general framework stemming from…

Missingness is a common issue for neuroimaging data, and neglecting it in downstream statistical analysis can introduce bias and lead to misguided inferential conclusions. It is therefore crucial to conduct appropriate statistical methods…

Testing conditional independence between two random vectors given a third is a fundamental and challenging problem in statistics, particularly in multivariate nonparametric settings due to the complexity of conditional structures. We…

This paper introduces an innovative method for conducting conditional independence testing in high-dimensional data, facilitating the automated discovery of significant associations within distinct subgroups of a population, all while…

Independence testing plays a central role in statistical and causal inference from observational data. Standard independence tests assume that the data samples are independent and identically distributed (i.i.d.) but that assumption is…

Multiple testing is a fundamental problem in high-dimensional statistical inference. Although many methods have been proposed to control false discoveries, it is still a challenging task when the tests are correlated to each other. To…

Conditional independence is a fundamental concept in many areas of statistical research, including, for example, sufficient dimension reduction, causal inference, and statistical graphical models. In many modern applications, data arise in…

Causal discovery is to learn cause-effect relationships among variables given observational data and is important for many applications. Existing causal discovery methods assume data sufficiency, which may not be the case in many real world…

Multiple hypothesis testing is a fundamental problem in high dimensional inference, with wide applications in many scientific fields. In genome-wide association studies, tens of thousands of tests are performed simultaneously to find if any…

One of the central objectives of modern risk management is to find a set of risks where the probability of multiple simultaneous catastrophic events is negligible. That is, risks are taken only when their joint behavior seems sufficiently…

This paper proposes a framework for semantic hypothesis testing tailored to imaging inverse problems. Modern imaging methods struggle to support hypothesis testing, a core component of the scientific method that is essential for the…

To understand how neural networks process information, it is important to investigate how neural network dynamics varies with respect to different stimuli. One challenging task is to design efficient statistical approaches to analyze…

Mutual independence is a key concept in statistics that characterizes the structural relationships between variables. Existing methods to investigate mutual independence rely on the definition of two competing models, one being nested into…

We provide a unified framework for independence and mean independence tests based on the Hilbert-Schmidt independence criterion, extending some previous results in the literature to hold in general topological spaces. We also present a…