Related papers: Concentration inequalities and asymptotic results …
We investigate densities of vaguely continuous convolution semigroups of probability measures on $\mathbb{R}^d$. We expose that many typical conditions on the characteristic exponent repeatedly used in the literature of the subject are…
Let $G$ be a sofic group, and let $\Sigma = (\sigma_n)_{n\geq 1}$ be a sofic approximation to it. For a probability-preserving $G$-system, a variant of the sofic entropy relative to $\Sigma$ has recently been defined in terms of sequences…
Suppose (standardized) measurements or statistics are monitored to raise an alarm when a threshold is exceeded. Often, the underlying population is heterogenous with respect to important discrete variables and thus samples may consist of…
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,…
Slepian and Sudakov-Fernique type inequalities, which compare expectations of maxima of Gaussian random vectors under certain restrictions on the covariance matrices, play an important role in probability theory, especially in empirical…
For an ergodic Brownian diffusion with invariant measure $\nu$, we consider a sequence of empirical distributions ($\nu$n) n$\ge$1 associated with an approximation scheme with decreasing time step ($\gamma$n) n$\ge$1 along an adapted…
Simultaneous statistical inference has been a cornerstone in the statistics methodology literature because of its fundamental theory and paramount applications. The mainstream multiple testing literature has traditionally considered two…
We use a non-linear characterization of orthonormal polynomials due to Saff in order to show that the behavior of orthonormal polynomials is determined only by its leading coefficient and its normalization. Several applications of this…
We consider a family of stochastic processes $\{X_t^\epsilon, t \in T\}$ on a metric space $T$, with a parameter $\epsilon \downarrow 0$. We study the conditions under which \lim_{\e \to 0} \P \Big(\sup_{t \in T} |X_t^\e| < \delta \Big) =1…
In centralized, distributed, and federated learning with stochastic gradients and $n$ workers, it was recently shown that it is infeasible to find an $\varepsilon$-stationary point faster than $\tilde{\Omega}\left(\min\left\{\frac{d \kappa…
We introduce an empirical functional $\Psi$ that is an optimal uniform mean estimator: Let $F\subset L_2(\mu)$ be a class of mean zero functions, $u$ is a real valued function, and $X_1,\dots,X_N$ are independent, distributed according to…
The distributional single index model is a semiparametric regression model in which the conditional distribution functions $P(Y \leq y | X = x) = F_0(\theta_0(x), y)$ of a real-valued outcome variable $Y$ depend on $d$-dimensional…
We provide a criterion for establishing lower bounds on the rate of convergence in $f$-variation of a continuous-time ergodic Markov process to its invariant measure. The criterion consists of novel super- and submartingale conditions for…
We provide upper bounds of the expected Wasserstein distance between a probability measure and its empirical version, generalizing recent results for finite dimensional Euclidean spaces and bounded functional spaces. Such a generalization…
Starting from concentration of measure hypotheses on $m$ random vectors $Z_1,\ldots, Z_m$, this article provides an expression of the concentration of functionals $\phi(Z_1,\ldots, Z_m)$ where the variations of $\phi$ on each variable…
We derive concentration inequalities for functions of the empirical measure of large random matrices with infinitely divisible entries and, in particular, stable ones. We also give concentration results for some other functionals of these…
In the past decades, weak convergence theory for stochastic processes has become a standard tool for analyzing the asymptotic properties of various statistics. Routinely, weak convergence is considered in the space of bounded functions…
Concentration properties of functionals of general Poisson processes are studied. Using a modified $\Phi$-Sobolev inequality a recursion scheme for moments is established, which is of independent interest. This is applied to derive moment…
We study Markov processes on weighted directed hypergraphs where the state of at most one vertex can change at a time. Our setting is general enough to include simplicial epidemic processes, processes on multilayered networks or even the…
We develop a new framework for deriving time-uniform concentration bounds for the output of stochastic sequential algorithms satisfying certain recursive inequalities akin to those defining the almost-supermartingale processes introduced by…