相关论文: Asymptotic normality of the $L_k$-error of the Gre…

We propose a novel statistical test to assess the mutual independence of multidimensional random vectors. Our approach is based on the $L_1$-distance between the joint density function and the product of the marginal densities associated…

This paper develops asymptotic normality results for individual coordinates of robust M-estimators with convex penalty in high-dimensions, where the dimension $p$ is at most of the same order as the sample size $n$, i.e, $p/n\le\gamma$ for…

This paper concerns the asymptotic behavior of a random variable $W_\lambda$ resulting from the summation of the functionals of a Gibbsian spatial point process over windows $Q_\lambda \uparrow R^d$. We establish conditions ensuring that…

Asymptotics for Dickman's number theoretic function $\rho(u)$, as $u \rightarrow \infty$, were given de Bruijn and Alladi, and later in sharper form by Hildebrand and Tenenbaum. The perspective in these works is that of analytic number…

Denote by $p(k)$ the limit, as $n \rightarrow \infty$, of the probability that a random permutation on a set of size $n$ has an invariant set of size $k$. We give an asymptotic formula for $p(k)$, showing that it is asymptotically…

We study here the random fluctuations in the number of critical points with values in an interval $I\subset \mathbb{R}$ for Gaussian spherical eigenfunctions $\left\{f_{\ell }\right\} $, in the high energy regime where $\ell \rightarrow…

In this paper we provide the asymptotic theory of the general of $\phi$-divergences measures, which includes the most common divergence measures : Renyi and Tsallis families and the Kullback-Leibler measure. Instead of using the Parzen…

This paper is concerned with estimation and inference for the location of a change point in the mean of independent high-dimensional data. Our change point location estimator maximizes a new U-statistic based objective function, and its…

Bayesian inference requires approximation methods to become computable, but for most of them it is impossible to quantify how close the approximation is to the true posterior. In this work, we present a theorem upper-bounding the KL…

In recent papers it has been demonstrated that sampling a Gibbs distribution from an appropriate time-irreversible Langevin process is, from several points of view, advantageous when compared to sampling from a time-reversible one. Adding…

We consider random walks with independent but not necessarily identical distributed increments. Assuming that the increments satisfy the well-known Lindeberg condition, we investigate the asymptotic behaviour of first-passage times over…

The infinite Brownian loop on a Riemannian manifold is the limit in distribution of the Brownian bridge of length $T$ around a fixed origin when $T \rightarrow +\infty$. The aim of this note is to study its long-time asymptotics on…

Let $K_n$ be the convex hull of i.i.d. random variables distributed according to the standard normal distribution on $\R^d$. We establish variance asymptotics as $n \to \infty$ for the re-scaled intrinsic volumes and $k$-face functionals of…

While the asymptotic normality of the maximum likelihood estimator under regularity conditions is long established, this paper derives explicit bounds for the bounded Wasserstein distance between the distribution of the maximum likelihood…

Given a low-frequency sample of the infinitely divisible moving average random field $\{\int_{\mathbb{R}^d}f(t-x)\Lambda (dx), t\in \mathbb{R}^d\}$, in [13] we proposed an estimator $\hat{uv_0}$ for the function $\mathbb{R}\ni x\mapsto…

We analyze the differences between the horizontal and the vertical component of the simple random walk on the 2-dimensional comb. In particular we evaluate by combinatorial methods the asymptotic behaviour of the expected value of the…

This paper is aimed to study the ergodic short-term behaviour of discretizations of circle expanding maps. More precisely, we prove some asymptotics of the distance between the $t$-th iterate of Lebesgue measure by the dynamics $f$ and the…

Using the inner product formula of the canonical Hilbert space of fractional Brownian motion on an interval $[0,T]$ with Hurst parameter $H\in (0,1)$ given by Alazemi et al., we show the asymptotic expansion of the norm of…

We study statistical inference for the optimal transport (OT) map (also known as the Brenier map) from a known absolutely continuous reference distribution onto an unknown finitely discrete target distribution. We derive limit distributions…

This paper establishes the Local Asymptotic Normality (LAN) property for the mixed fractional Brownian motion under high-frequency observations with Hurst index $H \in (0, 3/4)$. The simultaneous estimation of the volatility and the Hurst…