Related papers: Asymptotic Coupling and Its Applications in Inform…
Approximate Bayesian computation allows for statistical analysis in models with intractable likelihoods. In this paper we consider the asymptotic behaviour of the posterior distribution obtained by this method. We give general results on…
In this paper, we consider the problem of testing the equality of two multivariate distributions based on geometric graphs constructed using the interpoint distances between the observations. These include the tests based on the minimum…
During the past decades, the Ising distribution has attracted interest in many applied disciplines, as the maximum entropy distribution associated to any set of correlated binary (`spin') variables with observed means and covariances.…
In this review paper, we describe the use of couplings in several different mathematical problems. We consider the total variation norm, maximal coupling, and the $\bar{d}$-distance. We present a detailed proof of a result recently proved:…
A parameter estimation problem is considered, in which dispersed sensors transmit to the statistician partial information regarding their observations. The sensors observe the paths of continuous semimartingales, whose drifts are linear…
We propose nonparametric identification and semiparametric estimation of joint potential outcome distributions in the presence of confounding. First, in settings with observed confounding, we derive tighter, covariate-informed bounds on the…
We study the problem of maximizing the probability that (i) an electric component or financial institution $X$ does not default before another component or institution $Y$ and (ii) that $X$ and $Y$ default jointly within the class of all…
This paper investigates the problem of guessing subject to distortion, which was introduced by Arikan and Merhav. While the primary concern of the previous study was asymptotic analysis, our primary concern is non-asymptotic analysis. We…
This paper is devoted to the stochastic approximation of entropically regularized Wasserstein distances between two probability measures, also known as Sinkhorn divergences. The semi-dual formulation of such regularized optimal…
Extrapolation is a generic problem in physics and mathematics: how to use asymptotic data in one parametric regime to learn about the behavior of a function in another parametric regime. For example: extending weak coupling expansions to…
The Peaks Over Threshold (POT) method is the most popular statistical method for the analysis of univariate extremes. Even though there is a rich applied literature on Bayesian inference for the POT, the asymptotic theory for such proposals…
Systems of a large number N of globally coupled maps have become popular as a relatively simple prototype of high-dimensional dynamics, showing many interesting and typical phenomena like synchronisation, cluster formation and…
Consider large signal-plus-noise data matrices of the form $S + \Sigma^{1/2} X$, where $S$ is a low-rank deterministic signal matrix and the noise covariance matrix $\Sigma$ can be anisotropic. We establish the asymptotic joint distribution…
Detecting weak, systematic distribution shifts and quantitatively modeling individual, heterogeneous responses to policies or incentives have found increasing empirical applications in social and economic sciences. Given two probability…
Exact formulas are derived for the probability density functions of the sum and difference of two independent non-central gamma distributed random variables, with both series and integral representations of the density presented. These…
In time series analysis, statistics based on collections of estimators computed from sub-samples play a crucial role in an increasing variety of important applications. Proving results about the joint asymptotic distribution of such…
We study the validity of the time-dependent asymptotic $P_N$ approximation in radiative transfer of photons. The time-dependent asymptotic $P_N$ is an approximation which uses the standard $P_N$ equations with a closure that is based on the…
We consider the dynamics of a periodic chain of N coupled overdamped particles under the influence of noise. Each particle is subjected to a bistable local potential, to a linear coupling with its nearest neighbours, and to an independent…
If we have a system of binary variables and we measure the pairwise correlations among these variables, then the least structured or maximum entropy model for their joint distribution is an Ising model with pairwise interactions among the…
In this paper, we consider asymptotics of the optimal value and the optimal solutions of parametric minimax estimation problems. Specifically, we consider estimators of the optimal value and the optimal solutions in a sample minimax problem…