Related papers: On Exponential Convergence of Random Variables
The paper considers so-called adaptive estimations of regression, distribution density and spectral density of a Gaussian stationary sequence, asymptotically optimal in order at a growing number of observation on any regular subspace…
Real-world data often exhibits sequential dependence, across diverse domains such as human behavior, medicine, finance, and climate modeling. Probabilistic methods capture the inherent uncertainty associated with prediction in these…
Recently, authors have studied inequalities involving expectations of selected functions viz. failure rate, mean residual life, aging intensity function and log-odds rate which are defined for left truncated random variables in reliability…
Sequential monitoring of randomized trials traditionally relies on parametric assumptions or asymptotic approximations. We discuss a family of nonparametric sequential tests - collectively called e-RT - for binary, event-only, and…
The paper presents sufficient conditions of predictability for continuous time processes in deterministic setting. We found that processes with exponential decay on energy for higher frequencies are predictable in some weak sense on some…
The classical random matrix theory is mostly focused on asymptotic spectral properties of random matrices as their dimensions grow to infinity. At the same time many recent applications from convex geometry to functional analysis to…
Time-to-event models are a popular tool to analyse data where the outcome variable is the time to the occurrence of a specific event of interest. Here we focus on the analysis of time-to-event outcomes that are either intrisically discrete…
We study the convergence rates of empirical Bayes posterior distributions for nonparametric and high-dimensional inference. We show that as long as the hyperparameter set is discrete, the empirical Bayes posterior distribution induced by…
In this paper, we investigate the exponential ergodicity in a Wasserstein-type distance for a damping Hamiltonian dynamics with state-dependent and non-local collisions, which indeed is a special case of piecewise deterministic Markov…
This paper investigates risk measures derived from the expected maximum deficit in a continuous-time framework and develops optimal reserve allocation strategies across multiple lines of business. We formalize the expected maximum deficit…
In this paper, we study an ordinary differential equation with a degenerate global attractor at the origin, to which we add a white noise with a small parameter that regulates its intensity. Under general conditions, for any fixed…
The recurrence times between extreme events have been the central point of statistical analyses in many different areas of science. Simultaneously, the Poincar\'e recurrence time has been extensively used to characterize nonlinear dynamical…
We consider the safety evaluation of discrete time, stochastic systems over a finite horizon. Therefore, we discuss and link probabilistic invariance with reachability as well as reach-avoid problems. We show how to efficiently compute…
Consider a sample of a centered random vector with unit covariance matrix. We show that under certain regularity assumptions, and up to a natural scaling, the smallest and the largest eigenvalues of the empirical covariance matrix converge,…
We study models of continuous time, symmetric, $\Z^d$-valued random walks in random environments. One of our aims is to derive estimates on the decay of transition probabilities in a case where a uniform ellipticity assumption is absent. We…
We provide non-asymptotic bounds for the well-known temporal difference learning algorithm TD(0) with linear function approximators. These include high-probability bounds as well as bounds in expectation. Our analysis suggests that a…
An important question in statistical network analysis is how to estimate models of discrete and dependent network data with intractable likelihood functions, without sacrificing computational scalability and statistical guarantees. We…
We propose two new conformity scores for conformal prediction, in a general multivariate regression framework. The underlying score functions are based on a covariance analysis of the residuals and the input points. We give theoretical…
We focus on the problem estimating a monotone trend function under additive and dependent noise. New point-wise confidence interval estimators under both short- and long-range dependent errors are introduced and studied. These intervals are…
For a linear combination of random variables, fix some confidence level and consider the quantile of the combination at this level. We are interested in the partial derivatives of the quantile with respect to the weights of the random…