Related papers: Asymptotics of the Empirical Cross-over Function
In previous papers, we studied the asymptotic behaviour of $S_N(A,X)=(2N+1)^{-d/2}\sum_{n \in A_N} X_n,$ where $X$ is a centered, stationary and weakly dependent random field, and $A_N=A \cap [-N,N]^d$, $A \subset \mathbb{Z}^d$. This leads…
We study the asymptotic behavior of a family of functionals which penalize a short-range interaction of convolution type between a finite perimeter set and its complement. We first compute the pointwise limit and we obtain a lower estimate…
In this note, we establish an asymptotic expansion for the centering parameter appearing in the central limit theorems for linear spectral statistic of large-dimensional sample covariance matrices when the population has a spiked covariance…
In order to obtain functional limit theorems for heavy tailed stationary processes arising from dynamical systems, one needs to understand the clustering patterns of the tail observations of the process. These patterns are well described by…
Motivated by recent progress on the scaling behavior of entanglement entropy, we study the scaling behavior of the number of clusters crossing the boundary between two subsystems for several classical statistical models in two dimension.…
In terms of log canonical threshold, we characterize plurisubharmonic functions with logarithmic asymptotical behaviour.
We show that there exists a very natural, superstatistics-linked extension of the central limit theorem (CLT) to deformed exponentials (also called q-Gaussians): This generalization favorably compares with the one provided by S. Umarov and…
We study the convergence in distribution norms in the Central Limit Theorem for non identical distributed random variables that is $$ \varepsilon_{n}(f):={\mathbb{E}}\Big(f\Big(\frac 1{\sqrt…
Asymptotic expansions are derived for the tail distribution of the product of two correlated normal random variables with non-zero means and arbitrary variances, and more generally the sum of independent copies of such random variables.…
We derive theorems which outline explicit mechanisms by which anomalous scaling for the probability density function of the sum of many correlated random variables asymptotically prevails. The results characterize general anomalous scaling…
For testing the statistical significance of a treatment effect, we usually compare between two parts of a population, one is exposed to the treatment, and the other is not exposed to it. Standard parametric and nonparametric two-sample…
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…
We consider the problem of clustering functional data while jointly selecting the most relevant features for classification. This problem has never been tackled before in the functional data context, and it requires a proper definition of…
In this document we achieve exact and asymptotic enumeration of words, compositions over a finite group, and/or integer compositions characterized by local restrictions and, separately, subsequence pattern avoidance. We also count…
Strong consistency and asymptotic normality of the Quasi-Maximum Likelihood Estimator (QMLE) are given for a general class of multidimensional causal processes. For particular cases already studied in the literature (for instance univariate…
Many clustering schemes are defined by optimizing an objective function defined on the partitions of the underlying set of a finite metric space. In this paper, we construct a framework for studying what happens when we instead impose…
The paper is devoted to tests for uniformity based on sum-functions of overlapping spacings, where the order of spacings can diverge to infinity as the sample size increases. In particular, it is shown that the asymptotic local power of…
The aim of this work is to illustrate a conditional result involving the exponential sums over primes in short intervals under the assumption that both the Generalized Riemann Hypothesis and the Density Hypothesis for Dirichlet…
We introduce a new clustering method for the classification of functional data sets by their probabilistic law, that is, a procedure that aims to assign data sets to the same cluster if and only if the data were generated with the same…
By introducing Crossing functions and hyper-parameters I show that the Bayesian interpretation of the Crossing Statistics [1] can be used trivially for the purpose of model selection among cosmological models. In this approach to falsify a…