Related papers: Independence by Random Scaling
It is well known that when a pair of random variables is statistically independent, it has no-correlation (zero covariance, $E[XY] - E[X]E[Y] = 0$), and that the converse is not true. However, if both of these random variables take only two…
For a set of dependent random variables, without stationary or the strong mixing assumptions, we derive the asymptotic independence between their sums and maxima. Then we apply this result to high-dimensional testing problems, where we…
It is well known that an extreme order statistic and a central order statistic (os) as well as an intermediate os and a central os from a sample of iid univariate random variables get asymptotically independent as the sample size increases.…
The ratio $P(S_n=x)/P(Z_n=x)$ is investigated for three cases: (a) when $S_n$ is a sum of 1-dependent non-negative integer-valued random variables (rvs), satisfying some moment conditions, and $Z_n$ is Poisson rv; (b) when $S_n$ is a…
In this note we prove a large deviation bound on the sum of random variables with the following dependency structure: there is a dependency graph $G$ with a bounded chromatic number, in which each vertex represents a random variable.…
Identifying dependency in multivariate data is a common inference task that arises in numerous applications. However, existing nonparametric independence tests typically require computation that scales at least quadratically with the sample…
Structural independence is the (conditional) independence that arises from the structure rather than the precise numerical values of a distribution. We develop this concept and relate it to $d$-separation and structural causal models.…
We introduce a test for the conditional independence of random variables $X$ and $Y$ given a random variable $Z$, specifically by sampling from the joint distribution $(X,Y,Z)$, binning the support of the distribution of $Z$, and conducting…
The independence clustering problem is considered in the following formulation: given a set $S$ of random variables, it is required to find the finest partitioning $\{U_1,\dots,U_k\}$ of $S$ into clusters such that the clusters…
The random walk in Dirichlet environment is a random walk in random environment where the transition probabilities are independent Dirichlet random variables. This random walk exhibits a property of statistical invariance by time-reversal…
This paper develops an intuitive concept of perfect dependence between two variables of which at least one has a nominal scale. Perfect dependence is attainable for all marginal distributions. It furthermore proposes a set of dependence…
We propose an estimator of the Hilbert-Schmidt Independence Criterion obtained from an appropriate modification of the usual estimator. We then get asymptotic normality of this estimator both under independence hypothesis and under the…
We give necessary and sufficient conditions for two sub-vectors of a random vector with a multivariate extreme value distribution, corresponding to the limit distribution of the maximum of a multidimensional stationary sequence with…
Independent random signs can govern various discrete models that converge to non-isomorphic continuous limits. Convergence of Fourier-Walsh spectra is established under appropriate conditions.
In this paper we propose several variants to perform the independence test between two random elements based on recurrence rates. We will show how to calculate the test statistic in each one of these cases. From simulations we obtain that…
We obtain an almost sure bound for oscillation rates of empirical distribution functions for stationary causal processes. For short-range dependent processes, the oscillation rate is shown to be optimal in the sense that it is as sharp as…
The goal of this paper is to integrate the notions of stochastic conditional independence and variation conditional independence under a more general notion of extended conditional independence. We show that under appropriate assumptions…
A coefficient is introduced that quantifies the extent of separation of a random variable $Y$ relative to a number of variables $\mathbf{X} = (X_1, \dots, X_p)$ by skillfully assessing the sensitivity of the relative effects of the…
We introduce a novel measure of dependence that captures the extent to which a random variable $Y$ is determined by a random vector $X$. The measure equals zero precisely when $Y$ and $X$ are independent, and it attains one exactly when $Y$…
(To appear in The American Statistician.) Distance covariance (Sz\'ekely, Rizzo, and Bakirov, 2007) is a fascinating recent notion, which is popular as a test for dependence of any type between random variables $X$ and $Y$. This approach…