Related papers: A Neural Network-Based Approach to Normality Testi…

The assumption of normality has underlain much of the development of statistics, including spatial statistics, and many tests have been proposed. In this work, we focus on the multivariate setting and first review the recent advances in…

This paper proposes a novel test method for high-dimensional mean testing regard for the temporal dependent data. Comparison to existing methods, we establish the asymptotic normality of the test statistic without relying on restrictive…

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…

In this paper, we focus on the problem of statistical dependence estimation using characteristic functions. We propose a statistical dependence measure, based on the maximum-norm of the difference between joint and product-marginal…

Most normality tests in the literature are performed for scalar and independent samples. Thus, they become unreliable when applied to colored processes, hampering their use in realistic scenarios.We focus on Mardia's multivariate kurtosis,…

Network analysis is often focused on characterizing the dependencies between network relations and node-level attributes. Potential relationships are typically explored by modeling the network as a function of the nodal attributes or by…

Testing for normality is a widely used procedure in statistics and data analysis, often applied prior to employing methods that rely on the assumption of normally distributed data. While several existing tests target distributional…

Many statistical methodologies for high-dimensional data assume the population is normal. Although a few multivariate normality tests have been proposed, to the best of our knowledge, none of them can properly control the type I error when…

Neural networks are powerful predictive models, but they provide little insight into the nature of relationships between predictors and outcomes. Although numerous methods have been proposed to quantify the relative contributions of input…

Brain connectivity analysis is now at the foreground of neuroscience research. A connectivity network is characterized by a graph, where nodes represent neural elements such as neurons and brain regions, and links represent statistical…

In this article, we consider the problem of simultaneous testing of hypotheses when the individual test statistics are not necessarily independent. Specifically, we consider the problem of simultaneous testing of point null hypotheses…

The network data has attracted considerable attention in modern statistics. In research on complex network data, one key issue is finding its underlying connection structure given a network sample. The methods that have been proposed in…

Network data is a major object data type that has been widely collected or derived from common sources such as brain imaging. Such data contains numeric, topological, and geometrical information, and may be necessarily considered in certain…

Deciphering the associations between network connectivity and nodal attributes is one of the core problems in network science. The dependency structure and high-dimensionality of networks pose unique challenges to traditional dependency…

Conditional independence testing is a fundamental problem underlying causal discovery and a particularly challenging task in the presence of nonlinear and high-dimensional dependencies. Here a fully non-parametric test for continuous data…

The test of independence is a crucial component of modern data analysis. However, traditional methods often struggle with the complex dependency structures found in high-dimensional data. To overcome this challenge, we introduce a novel…

Applications of neural networks to data analyses in natural sciences are complicated by the fact that many inputs are subject to systematic uncertainties. To control the dependence of the neural network function to variations of the input…

We propose a simple multivariate normality test based on Kac-Bernstein's characterization, which can be conducted by utilising existing statistical independence tests for sums and differences of data samples. We also perform its empirical…

Normalizing flows are powerful non-parametric statistical models that function as a hybrid between density estimators and generative models. Current learning algorithms for normalizing flows assume that data points are sampled…

Comparing two population means of network data is of paramount importance in a wide range of scientific applications. Many existing network inference solutions focus on global testing of entire networks, without comparing individual network…