Related papers: Uniform error bounds for a continuous approximatio…

Hyperbolic balance laws with uncertain (random) parameters and inputs are ubiquitous in science and engineering. Quantification of uncertainty in predictions derived from such laws, and reduction of predictive uncertainty via data…

Nonlinear mixed effects models have received a great deal of attention in the statistical literature in recent years because of their flexibility in handling longitudinal studies, including human immunodeficiency virus viral dynamics,…

We present a fully computable a posteriori error estimator for piecewise linear finite element approximations of reaction-diffusion problems with mixed boundary conditions and piecewise constant reaction coefficient formulated in arbitrary…

A standard approach to computing expectations with respect to a given target measure is to introduce an overdamped Langevin equation which is reversible with respect to the target distribution, and to approximate the expectation by a…

We develop a uniform inference theory for high-dimensional slope parameters in threshold regression models, allowing for either cross-sectional or time series data. We first establish oracle inequalities for prediction errors, and L1…

This paper investigates the large sample properties of local regression distribution estimators, which include a class of boundary adaptive density estimators as a prime example. First, we establish a pointwise Gaussian large sample…

We establish general conditions under which there exists uniform in time convergence between a stochastic process and its approximated system. These standardised conditions consist of a local in time estimate between the original and the…

We study approximation of non-autonomous linear differential equations with variable delay over infinite intervals. We use piecewise constant argument to obtain a corresponding discrete difference equation. The study of numerical…

In this paper we propose a wide class of truncated stochastic approximation procedures with moving random bounds. While we believe that the proposed class of procedures will find its way to a wider range of applications, the main motivation…

In this paper we derive tail bounds on the norms of random submatrices with non-uniformly distributed supports. We apply these results to sparse approximation and conduct an analysis of the average case performance of thresholding,…

The method to derive uniform bounds with Gaussian and Rademacher complexities is extended to the case where the sample average is replaced by a nonlinear statistic. Tight bounds are obtained for U-statistics, smoothened L-statistics and…

We derive asymptotic formulas for central extended binomial coefficients, which are generalizations of binomial coefficients. To do so, we relate the exact distribution of the sum of independent discrete uniform random variables to the…

We consider the asymptotic behavior of the incomplete gamma functions gamma(-a,-z) and Gamma(-a,-z) as a goes to infinity. Uniform expansions are needed to describe the transition area z~a in which case error functions are used as main…

We consider the Grenander estimator that is the maximum likelihood estimator for non-increasing densities. We prove uniform central limit theorems for certain subclasses of bounded variation functions and for H\"older balls of smoothness…

We study the empirical likelihood approach to construct confidence intervals for the optimal value and the optimality gap of a given solution, henceforth quantify the statistical uncertainty of sample average approximation, for optimization…

In this work, we consider the numerical solution of an initial boundary value problem for the distributed order time fractional diffusion equation. The model arises in the mathematical modeling of ultra-slow diffusion processes observed in…

We study a general framework of distributional computational graphs: computational graphs whose inputs are probability distributions rather than point values. We analyze the discretization error that arises when these graphs are evaluated…

Sampling-based motion planners (SBMPs) are widely used to compute dynamically feasible robot paths. However, their reliance on uniform sampling often leads to poor efficiency and slow planning in complex environments. We introduce a novel…

We provide a general method to analyze the asymptotic properties of a variety of estimators of continuous time diffusion processes when the data are not only discretely sampled in time but the time separating successive observations may…

In this paper, we establish uniform asymptotic certainty bands for the conditional cumulative distribution function. To this aim, we give exact rate of strong uniform consistency for the local linear estimator of this function. The…