Related papers: Analysis of multivariate symbol statistics in prim…
Social sampling is a novel randomized message passing protocol inspired by social communication for opinion formation in social networks. In a typical social sampling algorithm, each agent holds a sample from the empirical distribution of…
A key aspect where extreme values methods differ from standard statistical models is through having asymptotic theory to provide a theoretical justification for the nature of the models used for extrapolation. In multivariate extremes many…
Consider the ideal I corresponding to r points in P^2. We study the symbolic generic initial system of I, formed by taking the generic initial ideals of the symbolic powers of I, and its asymptotic behaviour. In particular, we describe the…
We develop asymptotic approximations that can be applied to sequential estimation and inference problems, adaptive randomized controlled trials, and related settings. In batched adaptive settings where the decision at one stage can affect…
A variety of estimators for the parameters of the Generalized Pareto distribution, the approximating distribution for excesses over a high threshold, have been proposed, always assuming the underlying data to be independent. We recently…
Symmetry is a cornerstone of much of mathematics, and many probability distributions possess symmetries characterized by their invariance to a collection of group actions. Thus, many mathematical and statistical methods rely on such…
Asymptotic theory for M-estimation problems usually focuses on the asymptotic convergence of the sample descriptor, defined as the minimizer of the sample loss function. Here, we explore a related question and formulate asymptotic theory…
This work is concerned with the estimation of multidimensional regression and the asymptotic behaviour of the test involved in selecting models. The main problem with such models is that we need to know the covariance matrix of the noise to…
In this paper, we study inference for high-dimensional data characterized by small sample sizes relative to the dimension of the data. In particular, we provide an infinite-dimensional framework to study statistical models that involve…
Many results related to quantitative problems in the metric theory of Diophantine approximation are asymptotic, such as the number of rational solutions to certain inequalities grows with the same rate almost everywhere modulo an asymptotic…
We prove theorems about the Gaussian asymptotics of an empirical bridge built from linear model regressors with multiple regressor ordering. We study the testing of the hypothesis of a linear model for the components of a random vector: one…
This paper analyzes the limit properties of the empirical process of $\alpha$-stable random variables with long range dependence. The $\alpha$-stable random variables are constructed by non-linear transformations of bivariate sequences of…
We employ stabilization methods and second order Poincar\'e inequalities to establish rates of multivariate normal convergence for a large class of vectors $(H_s^{(1)},...,H_s^{(m)})$, $s \geq 1$, of statistics of marked Poisson processes…
Let $\xi_1, \xi_2,\ldots$ be a sequence of independent and identically distributed random variables with zero mean, finite second moment and regularly varying right distribution tail. Motivated by a stop-loss insurance model, we consider a…
Randomized experiments have become important tools in empirical research. In a completely randomized treatment-control experiment, the simple difference in means of the outcome is unbiased for the average treatment effect, and covariate…
If multiway cluster-robust standard errors are used routinely in applied economics, surprisingly few theoretical results justify this practice. This paper aims to fill this gap. We first prove, under nearly the same conditions as with…
This paper develops a theory of distribution- and time-uniform asymptotics, culminating in the first large-sample anytime-valid inference procedures that are shown to be uniformly valid in a rich class of distributions. Historically,…
In this paper we study the asymptotic theory for samples problem based on the functional empirical process (fep), this new method is called general samples problem. We suggest this method to develop the full theory of estimation of means,…
The purpose of the present paper is to establish moderate deviation principles for a rather general class of random variables fulfilling certain bounds of the cumulants. We apply a celebrated lemma of the theory of large deviations…
We consider covariance parameter estimation for Gaussian processes with functional inputs. From an increasing-domain asymptotics perspective, we prove the asymptotic consistency and normality of the maximum likelihood estimator. We extend…