Related papers: Ordinal pattern dependence as a multivariate depen…
The tetrad constraint is widely used to test whether four observed variables are conditionally independent given a latent variable, based on the fact that if four observed variables following a linear model are mutually independent after…
Classical and more recent tests for detecting distributional changes in multivariate time series often lack power against alternatives that involve changes in the cross-sectional dependence structure. To be able to detect such changes…
This paper is concerned with modeling the dependence structure of two (or more) time-series in the presence of a (possible multivariate) covariate which may include past values of the time series. We assume that the covariate influences…
Mutual information is fundamentally important for measuring statistical dependence between variables and for quantifying information transfer by signaling and communication mechanisms. It can, however, be challenging to evaluate for…
Distance correlation is a recent extension of Pearson's correlation, that characterises general statistical independence between Euclidean-space-valued random variables, not only linear relations. This review delves into how and when…
Recently established, directed dependence measures for pairs $(X,Y)$ of random variables build upon the natural idea of comparing the conditional distributions of $Y$ given $X=x$ with the marginal distribution of $Y$. They assign pairs…
In this paper we provide a theoretical analysis of counterfactual invariance. We present a variety of existing definitions, study how they relate to each other and what their graphical implications are. We then turn to the current major…
Statistical analysis of high-dimensional functional times series arises in various applications. Under this scenario, in addition to the intrinsic infinite-dimensionality of functional data, the number of functional variables can grow with…
In 2002, in a seminal article, Christoph Bandt and Bernd Pompe proposed a new methodology for the analysis of complex time series, now known as Ordinal Analysis. The ordinal methodology is based on the computation of symbols (known as…
In data science, it is often required to estimate dependencies between different data sources. These dependencies are typically calculated using Pearson's correlation, distance correlation, and/or mutual information. However, none of these…
A central issue in the theory of extreme values focuses on suitable conditions such that the well-known results for the limiting distributions of the maximum of i.i.d. sequences can be applied to stationary ones. In this context, the…
We derive the asymptotic distribution of ordinal-pattern frequencies under weak dependence conditions and investigate the long-run covariance matrix not only analytically for moving-average, Gaussian, and the novel generalized coin-tossing…
An ordinal view of independence is studied in the framework of possibility theory. We investigate three possible definitions of dependence, of increasing strength. One of them is the counterpart to the multiplication law in probability…
We investigate the problem of detecting dependencies between the components of a high-dimensional vector. Our approach advances the existing literature in two important respects. First, we consider the problem under privacy constraints.…
The study of causality or causal inference - how much a given treatment causally affects a given outcome in a population - goes way beyond correlation or association analysis of variables, and is critical in making sound data driven…
A simple approach for modeling multivariate extremes is to consider the vector of component-wise maxima and their max-stable distributions. The extremal dependence can be inferred by estimating the angular measure or, alternatively, the…
When observations are organized into groups where commonalties exist amongst them, the dependent random measures can be an ideal choice for modeling. One of the propositions of the dependent random measures is that the atoms of the…
This paper proposes a new mutual independence test for a large number of high dimensional random vectors. The test statistic is based on the characteristic function of the empirical spectral distribution of the sample covariance matrix. The…
Marginal structural models were introduced in order to provide estimates of causal effects from interventions based on observational studies in epidemiological research. The key point is that this can be understood in terms of Girsanov's…
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…