Related papers: On the error estimate for cubature on Wiener space

Cubature rules on the triangle have been extensively studied, as they are of great practical interest in numerical analysis. In most cases, the process by which new rules are obtained does not preclude the existence of similar rules with…

We present a new adaptive algorithm for learning discrete distributions under distribution drift. In this setting, we observe a sequence of independent samples from a discrete distribution that is changing over time, and the goal is to…

We derive integral and sup-estimates for the curvature of stably marginally outer trapped surfaces in a sliced space-time. The estimates bound the shear of a marginally outer trapped surface in terms of the intrinsic and extrinsic curvature…

The U,V method of estimation provides unbiased estimators or predictors of random quantities. The method was introduced by Robbins \citer3 and subsequently studied in a series of papers by Robbins and Zhang. (See Zhang \citer5.) Practical…

We study a class of Metropolis-Hastings algorithms for target measures that are absolutely continuous with respect to a large class of non-Gaussian prior measures on Banach spaces. The algorithm is shown to have a spectral gap in a…

We consider the problem of estimating curvature where the data can be viewed as a noisy sample from an underlying manifold. For manifolds of dimension greater than one there are multiple definitions of local curvature, each suggesting a…

Scatter in distance indicators introduces two conceptually distinct systematic biases when reconstructing peculiar velocity fields from redshifts and distances. The first is distance Malmquist bias (dMB) that affects individual distance…

In this manuscript we consider the problem of generalized linear estimation on Gaussian mixture data with labels given by a single-index model. Our first result is a sharp asymptotic expression for the test and training errors in the…

We study a regression characterization for the quadratic estimator of weak lensing, developed by Hu and Okamoto (2001,2002), for cosmic microwave background observations. This characterization motivates a modification of the quadratic…

Generalization error bounds are essential to understanding machine learning algorithms. This paper presents novel expected generalization error upper bounds based on the average joint distribution between the output hypothesis and each…

We consider robust covariance estimation with group symmetry constraints. Non-Gaussian covariance estimation, e.g., Tyler scatter estimator and Multivariate Generalized Gaussian distribution methods, usually involve non-convex minimization…

Missing data imputation, where a model is trained on observed data to estimate unobserved values, is a fundamental problem in machine learning. In this paper, we rigorously formulate imputation model learning as a mean-squared error risk…

We derive upper and lower estimates of the area of unknown defects in the form of either cavities or rigid inclusions in Mindlin-Reissner elastic plates in terms of the difference $\delta W$ of the works exerted by boundary loads on the…

Inverse problems use physical measurements along with a computational model to estimate the parameters or state of a system of interest. Errors in measurements and uncertainties in the computational model lead to inaccurate estimates. This…

Conventional algorithms for galaxy power spectrum estimation measure the true spectrum convolved with a survey window function, which, for parameter inference, must be compared with a similarly convolved theory model. In this work, we…

High dimensional integrals can be approximated well by quasi-Monte Carlo methods. However, determining the number of function values needed to obtain the desired accuracy is difficult without some upper bound on an appropriate semi-norm of…

Estimation of the prediction error of a linear estimation rule is difficult if the data analyst also use data to select a set of variables and construct the estimation rule using only the selected variables. In this work, we propose an…

In applications of centre manifold theory we need more flexible error estimates than that provided by, for example, the Approximation Theorem~3 by Carr (1981,1983). Here we extend the theory to cover the case where the order of…

A complete error analysis of variational integrators is obtained, by blowing up the discrete variational principles, all of which have a singularity at zero time-step. Divisions by the time step lead to an order that is one less than…

We present an asymptotic expansion formula of an estimator for the drift coefficient of the fractional Ornstein-Uhlenbeck process. As the machinery, we apply the general expansion scheme for Wiener functionals recently developed by the…