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For two independent, almost surely finite random variables, independence of their minimum (time) and the event that one of them is either greater, equal or less than the other (cause) is completely characterized. It is shown that, other…
Instrumental variables allow for quantification of cause and effect relationships even in the absence of interventions. To achieve this, a number of causal assumptions must be met, the most important of which is the independence assumption,…
We give two asymptotic results for the empirical distance covariance on separable metric spaces without any iid assumption on the samples. In particular, we show the almost sure convergence of the empirical distance covariance for any…
We study the problem of testing \emph{conditional independence} for discrete distributions. Specifically, given samples from a discrete random variable $(X, Y, Z)$ on domain $[\ell_1]\times[\ell_2] \times [n]$, we want to distinguish, with…
This paper is concerned with test of the conditional independence. We first establish an equivalence between the conditional independence and the mutual independence. Based on the equivalence, we propose an index to measure the conditional…
Dependency functions of dependent variables are relevant for i) performing uncertainty quantification and sensitivity analysis in presence of dependent variables and/or correlated variables, and ii) simulating random dependent variables. In…
We study the problem of empirical minimization for variance-type functionals over functional classes. Sharp non-asymptotic bounds for the excess variance are derived under mild conditions. In particular, it is shown that under some…
Instrumental variable models allow us to identify a causal function between covariates $X$ and a response $Y$, even in the presence of unobserved confounding. Most of the existing estimators assume that the error term in the response $Y$…
Let $\bigl\{X_k\bigr\}_{k \in \mathbb{Z}} \in \mathbb{L}^2(\mathcal{T})$ be a stationary process with associated lag operators ${\boldsymbol{\cal C}}_h$. Uniform asymptotic expansions of the corresponding empirical eigenvalues and…
We investigate approximating joint distributions of random processes with causal dependence tree distributions. Such distributions are particularly useful in providing parsimonious representation when there exists causal dynamics among…
Existing methods for the estimation of stable distribution parameters, such as those based on sample quantiles, sample characteristic functions or maximum likelihood generally assume an independent sample. Little attention has been paid to…
Suppose we observe an invertible linear process with independent mean-zero innovations and with coefficients depending on a finite-dimensional parameter, and we want to estimate the expectation of some function under the stationary…
Complex systems are often characterized by the interplay of multiple interconnected dynamical processes operating across a range of temporal scales. This phenomenon is widespread in both biological and artificial scenarios, making it…
We develop novel empirical Bernstein inequalities for the variance of bounded random variables. Our inequalities hold under constant conditional variance and mean, without further assumptions like independence or identical distribution of…
We report on the possibilities of using the method of normal fundamental systems for solving some problems of oscillation theory. Large elastic dynamical systems with continuous and discrete parameters are considered, which have many…
We study the work distribution of a single particle moving in a harmonic oscillator with time-dependent strength. This simple system has a non-Gaussian work distribution with exponential tails. The time evolution of the corresponding moment…
The subject of this paper is the elucidation of effects of actions from causal assumptions represented as a directed graph, and statistical knowledge given as a probability distribution. In particular, we are interested in predicting…
We consider a model system of persistent random walkers that can jam, pass through each other or jump apart (recoil) on contact. In a continuum limit, where particle motion between stochastic changes in direction becomes deterministic, we…
A function of the empirical characteristic function,exists for the stable distribution, which leads to a linear regression and can be used to estimate the parameters. Two approaches are often used, one to find optimal values of t, but these…
It is well known that the distribution of extreme values of strictly stationary sequences differ from those of independent and identically distributed sequences in that extremal clustering may occur. Here we consider non-stationary but…