Related papers: Uniform error bounds for a continuous approximatio…

In this paper, we develop a general machinery for finding explicit uniform probability and moment bounds on sub-additive positive functionals of random processes. Using the developed general technique, we derive uniform bounds on the…

We consider a type of nonnormal approximation of infinitely divisible distributions that incorporates compound Poisson, Gamma, and normal distributions. The approximation relies on achieving higher orders of cumulant matching, to obtain…

Here we research the univariate quantitative approximation of real and complex valued continuous functions on a compact interval or all the real line by quasi-interpolation, Baskakov type and quadrature type neural network operators. We…

We consider estimating the proportion of random variables for two types of composite null hypotheses: (i) the means of the random variables belonging to a non-empty, bounded interval; (ii) the means of the random variables belonging to an…

We develop approximate estimation methods for exponential random graph models (ERGMs), whose likelihood is proportional to an intractable normalizing constant. The usual approach approximates this constant with Monte Carlo simulations,…

Functions satisfying a defective renewal equation arise commonly in applied probability models. Usually these functions don't admit a explicit expression. In this work we consider to approximate them by means of a gamma-type operator given…

This paper provides statistical guarantees on the accuracy of dynamical models learned from dependent data sequences. Specifically, we develop uniform error bounds that apply to quantized models and imperfect optimization algorithms…

We obtain non-symmetric upper and lower bounds on the rate of convergence of general monotone approximation/numerical schemes for parabolic Hamilton Jacobi Bellman Equations by introducing a new notion of consistency. We apply our general…

We consider linear and obstacle problems driven by a nonlocal integral operator, for which nonlocal interactions are restricted to a ball of finite radius. These type of operators are used to model anomalous diffusion and, for a special…

This paper is devoted to the estimators of the mean that provide strong non-asymptotic guarantees under minimal assumptions on the underlying distribution. The main ideas behind proposed techniques are based on bridging the notions of…

We study the approximation of non-negative multi-variate couplings in the uniform norm while matching given single-variable marginal constraints.

By application of the theory for second-order linear differential equations with two turning points developed in \cite{Olver1975}, uniform asymptotic approximations are obtained for the Lam\'{e} and Mathieu functions with a large real…

Bounds of the accuracy of the normal approximation to the distribution of a sum of independent random variables are improved under relaxed moment conditions, in particular, under the absence of moments of orders higher than the second.…

Uniform convergence rates are provided for asymptotic representations of sample extremes. These bounds which are universal in the sense that they do not depend on the extreme value index are meant to be extended to arbitrary samples…

In this paper we improve some existing results concerning the approximation of the distribution of extremes of a 1-dependent and stationary sequence of random variables. We enlarge the range of applicability and improve the approximation…

We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…

Diffusion approximation provides weak approximation for stochastic gradient descent algorithms in a finite time horizon. In this paper, we introduce new tools motivated by the backward error analysis of numerical stochastic differential…

Stochastic iterative algorithms, including stochastic gradient descent (SGD) and stochastic gradient Langevin dynamics (SGLD), are widely utilized for optimization and sampling in large-scale and high-dimensional problems in machine…

Uniform deviation bounds limit the difference between a model's expected loss and its loss on an empirical sample uniformly for all models in a learning problem. As such, they are a critical component to empirical risk minimization. In this…

Asymptotic expansions are derived for solutions of the parabolic cylinder and Weber differential equations. In addition the inhomogeneous versions of the equations are considered, for the case of polynomial forcing terms. The expansions…