Related papers: Analytical Error Estimation of Conformal Mappings …
This paper addresses the problem of identifying and estimating the causal effect of a treatment in the presence of unmeasured confounding and various types of right-censoring. Examples of these censoring mechanisms are administrative…
High-dimensional compositional data arise naturally in many applications such as metagenomic data analysis. The observed data lie in a high-dimensional simplex, and conventional statistical methods often fail to produce sensible results due…
In this article, we consider a simple representation for real numbers and propose top-down procedures to approximate various algebraic and transcendental operations with arbitrary precision. Detailed algorithms and proofs are provided to…
Intensity estimation for Poisson processes is a classical problem and has been extensively studied over the past few decades. Practical observations, however, often contain compositional noise, i.e. a nonlinear shift along the time axis,…
Area-specific causal inference is important in many policy and survey applications, where the goal is to evaluate treatment effects for small geographic or demographic domains. Existing causal small area estimation methods, however,…
This work presents a new sufficient condition for synthesizing nonlinear controllers that yield bounded closed-loop tracking error transients despite the presence of unmatched uncertainties that are concurrently being learned online. The…
We consider mixed finite element approximation of a singularly perturbed fourth-order elliptic problem with two different boundary conditions, and present a new measure of the error, whose components are balanced with respect to the…
A posteriori error analysis is a technique to quantify the error in particular simulations of a numerical approximation method. In this article, we use such an approach to analyze how various error components propagate in certain moving…
We investigate a family of integrals involving modified Bessel functions that arise in the context of neutrino scattering. Recursive formulas are derived for evaluating these integrals and their asymptotic expansions are computed. We prove…
We consider a coupled system of two singularly perturbed reaction-diffusion equations, with two small parameters $0< \epsilon \le \mu \le 1$, each multiplying the highest derivative in the equations. The presence of these parameters causes…
We use analytic bootstrap techniques for a CFT with an interface or a boundary. Exploiting the analytic structure of the bulk and boundary conformal blocks we extract the CFT data. We further constrain the CFT data by applying the equation…
We consider the adaptive Lasso estimator with componentwise tuning in the framework of a low-dimensional linear regression model. In our setting, at least one of the components is penalized at the rate of consistent model selection and…
It is well known that carefully crafted imperceptible perturbations can cause state-of-the-art deep learning classification models to misclassify. Understanding and analyzing these adversarial perturbations play a crucial role in the design…
We consider a framework for determining and estimating the conditional pairwise relationships of variables when the observed samples are contaminated with measurement error in high dimensional settings. Assuming the true underlying…
This paper presents a convergence analysis of kernel-based quadrature rules in misspecified settings, focusing on deterministic quadrature in Sobolev spaces. In particular, we deal with misspecified settings where a test integrand is less…
An important challenge in statistical analysis lies in controlling the bias of estimators due to the ever-increasing data size and model complexity. Approximate numerical methods and data features like censoring and misclassification often…
This work is aimed at the derivation of reliable and efficient a posteriori error estimates for convection-dominated diffusion problems motivated by a linear Fokker-Planck problem appearing in computational neuroscience. We obtain…
Optimization problems, generalized equations, and the multitude of other variational problems invariably lead to the analysis of sets and set-valued mappings as well as their approximations. We review the central concept of set-convergence…
Individual treatment effects are not point-identified from data. The Probability of Necessity and Sufficiency (PNS) circumvents this limitation by characterizing individual-level causality through intersection bounds derived from combined…
We use a conformal mapping method introduced in a companion paper to study the properties of bi-harmonic fields in the vicinity of rough boundaries. We focus our analysis on two different situations where such bi-harmonic problems are…