Related papers: Asymptotic independence for unimodal densities
Conditional independence in a multivariate normal (or Gaussian) distribution is characterized by the vanishing of subdeterminants of the distribution's covariance matrix. Gaussian conditional independence models thus correspond to algebraic…
We consider the diffusion of independent particles experiencing random accelerations by a space- and time-dependent force as well as viscous damping. This model can exhibit several asymptotic behaviours, depending upon the limiting cases…
Let $F_n = (F_{1,n}, ....,F_{d,n})$, $n\geq 1$, be a sequence of random vectors such that, for every $j=1,...,d$, the random variable $F_{j,n}$ belongs to a fixed Wiener chaos of a Gaussian field. We show that, as $n\to\infty$, the…
The need to test whether two random vectors are independent has spawned a large number of competing measures of dependence. We are interested in nonparametric measures that are invariant under strictly increasing transformations, such as…
We consider the statistical experiment given by a sample of a stationary Gaussian process with an unknown smooth spectral density f. Asymptotic equivalence, in the sense of Le Cam's deficiency Delta-distance, to two Gaussian experiments…
We propose two model-free, permutation-based tests of independence between a pair of random variables. The tests can be applied to samples from any bivariate distribution: continuous, discrete or mixture of those, with light tails or heavy…
We introduce a nonparametric graphical model for discrete node variables based on additive conditional independence. Additive conditional independence is a three way statistical relation that shares similar properties with conditional…
Following our previous work on copula-based nonsymmetric bivariate dependence measures, we propose a new set of conditions on nonsymmetric multivariate dependence measures which characterize both independence and complete dependence of one…
The framework of geometric extremes is based on the convergence of scaled sample clouds onto a limit set, characterized by a gauge function, with the shape of the limit set determining extremal dependence structures. While it is known that…
The paper studies the asymptotic behaviour of weighted functionals of long-range dependent data over increasing observation windows. Various important statistics, including sample means, high order moments, occupation measures can be given…
In this paper we discuss the continuity properties of the integrated density of states for random models based on that of the single site distribution. Our results are valid for models with independent randomness with arbitrary free parts.…
We establish necessary and sufficient conditions for convergence (in the sense of finite dimensional distributions) of multiplicative measures on the set of partitions. We show that this convergence is equivalent to asymptotic independence…
Following our previous work on copula-based nonsymmetric dependence measures, we introduce similar measures for discrete random variables. The measures cover the range between two extremes: independence and complete dependence, which take…
Classical conditions for asymptotic stability of periodic solutions bifurcating from a limit cycle rely on the derivative of the corresponding bifurcation function F at the bifurcation point t. We show that for analytic systems this result…
The paper gives a general condition on permutations, condition under which a semicircular matrix is free independent, or asymptotically free independent from the semicircular matrix obtained by permuting its entries. In particular, it is…
In this paper we study the asymptotic theory for spectral analysis of stationary random fields, including linear and nonlinear fields. Asymptotic properties of Fourier coefficients and periodograms, including limiting distributions of…
The multivariate Hilbert-Schmidt-Independence-Criterion (dHSIC) and distance multivariance allow to measure and test independence of an arbitrary number of random vectors with arbitrary dimensions. Here we define versions which only depend…
In this article, we propose a new method for the fundamental task of testing for dependence between two groups of variables. The response densities under the null hypothesis of independence and the alternative hypothesis of dependence are…
We give asymptotics for the cumulative distribution function (CDF) for degrees of large dense random graphs sampled from a graphon. The proof is based on precise asymptotics for binomial random variables. Replacing the indicator function in…
Frequentist-style large-sample properties of Bayesian posterior distributions, such as consistency and convergence rates, are important considerations in nonparametric problems. In this paper we give an analysis of Bayesian asymptotics…