Related papers: Asymptotics of the Empirical Cross-over Function
An extension of the empirical copula is considered by combining an estimator of a multivariate cumulative distribution function with estimators of the marginal cumulative distribution functions for marginal estimators that are not…
We investigate the probability density of rescaled sums of iterates of deterministic dynamical systems, a problem relevant for many complex physical systems consisting of dependent random variables. A Central Limit Theorem (CLT) is only…
Exploratory data analysis is often used to test the goodness-of-fit of sample observations to specific target distributions. A few such graphical tools have been extensively used to detect subexponential or heavy-tailed behavior in observed…
A law of large numbers and a central limit theorem are derived for linear statistics of random symmetric matrices whose on-or-above diagonal entries are independent, but neither necessarily identically distributed, nor necessarily all of…
We consider supercritical branching random walks on transitive graphs and we prove a law of large numbers for the mean displacement of the ensemble of particles, and a Stam-type central limit theorem for the empirical distributions, thus…
We introduce the calculus of Classical Transitions (CT), which extends the research line on the relationship between linear logic and processes to labelled transitions. The key twist from previous work is registering parallelism in typing…
Extremes occur in stationary regularly varying time series as short periods with several large observations, known as extremal blocks. We study cluster statistics summarizing the behavior of functions acting on these extremal blocks.…
We consider a random field, defined on an integer-valued d-dimensional lattice, with covariance function satisfying a condition more general than summability. Such condition appeared in the well-known Newman's conjecture concerning the…
We show that a modified Empirical process converges to the limiting Gaussian process whenever the limit is continuous. The modification depends on the properties of the limit via Talagrand's characterization of the continuity of Gaussian…
We establish a central limit theorem for the fluctuations of the linear statistics in the $\beta$-ensemble of dimension $N$ at a temperature proportional to $N$ and with confining smooth potential. In this regime, the particles do not…
Using Bernstein polynomial approximations, we prove the central limit theorem for linear spectral statistics of sample covariance matrices, indexed by a set of functions with continuous fourth order derivatives on an open interval including…
A central limit theorem (CLT) for the smoothed empirical spectral distribution of sample covariance matrices is established. Moreover, the CLTs for the smoothed quantiles of Marcenko and Pastur's law have been also developed.
We develop new methods to integrate experimental and observational data in causal inference. While randomized controlled trials offer strong internal validity, they are often costly and therefore limited in sample size. Observational data,…
Given a sequence of integers $a_j, j\ge 1,$ a multiset is a combinatorial object composed of unordered components, such that there are exactly $a_j$ one-component multisets of size $j.$ When $a_j\asymp j^{r-1} y^j$ for some $r>0$, $y\geq…
This work develops central limit theorems for cross-validation and consistent estimators of its asymptotic variance under weak stability conditions on the learning algorithm. Together, these results provide practical, asymptotically-exact…
We consider Betti numbers of the excursion of a smooth Euclidean Gaussian field restricted to a rectangular window, in the asymptotics where the window grows to R^d . With motivations coming from Topological Data Analysis, we derive a…
This paper investigates the behavior of statistical ensembles under iteration map induced by discrete integrable Hamiltonian systems in deterministic case and stochastic case, addressing the problem from two perspectives: the Law of Large…
The object of study is the problem of testing for uniformity of the multinomial distribution. We consider tests based on symmetric statistics, defined as the sum of some function of cell-frequencies. Mainly, attention is focused on the…
$L$-ensembles are a class of determinantal point processes which can be viewed as a statistical mechanical systems in the grand canonical ensemble. Circulant $L$-ensembles are the subclass which are locally translationally invariant and…
We consider the spectral properties of a class of regularized estimators of (large) empirical covariance matrices corresponding to stationary (but not necessarily Gaussian) sequences, obtained by banding. We prove a law of large numbers…