Related papers: Non-stationary extremal eigenvalue approximations …
Recently, many machine learning and statistical models such as non-linear regressions, the Single Index, Multi-index, Varying Coefficient Index Models and Two-layer Neural Networks can be reduced to or be seen as a special case of a new…
We derive and discuss a posteriori error estimators for Galerkin and collocation IGA boundary element methods for weakly-singular integral equations of the first-kind in 2D. While recent own work considered the Faermann residual error…
This paper studies the problem of estimating the covariance of a collection of vectors using only highly compressed measurements of each vector. An estimator based on back-projections of these compressive samples is proposed and analyzed. A…
We develop a method for estimating well-conditioned and sparse covariance and inverse covariance matrices from a sample of vectors drawn from a sub-gaussian distribution in high dimensional setting. The proposed estimators are obtained by…
We present an a posteriori error estimate based on equilibrated stress reconstructions for the finite element approximation of a unilateral contact problem with weak enforcement of the contact conditions. We start by proving a guaranteed…
In this paper, we study non-asymptotic deviation bounds of the least squares estimator in Gaussian AR($n$) processes. By relying on martingale concentration inequalities and a tail-bound for $\chi^2$ distributed variables, we provide a…
In this paper, we address the efficient implementation of moving horizon state estimation of constrained discrete-time linear systems. We propose a novel iteration scheme which employs a proximity-based formulation of the underlying…
Statistical inference for time series such as curve estimation for time-varying models or testing for existence of change-point have garnered significant attention. However, these works are generally restricted to the assumption of…
We introduce and explain key relations between a posteriori error estimates and subspace correction methods viewed as preconditioners for problems in infinite dimensional Hilbert spaces. We set the stage using the Finite Element Exterior…
We analyze the convergence of the Conjugate Gradient (CG) method in exact arithmetic, when the coefficient matrix $A$ is symmetric positive semidefinite and the system is consistent. To do so, we diagonalize $A$ and decompose the algorithm…
The explicit formula for the elements of the successive intermediate matrices of the Gauss-Jordan elimination procedure for the solution of systems of linear equations is applied to error analysis. Stability conditions in terms of relative…
We describe a strategy for solving nonlinear eigenproblems numerically. Our approach is based on the approximation of a vector-valued function, defined as solution of a non-homogeneous version of the eigenproblem. This approximation step is…
A posteriori error estimates are an important tool to bound discretization errors in terms of computable quantities avoiding regularity conditions that are often difficult to establish. For non-linear and non-differentiable problems,…
In a companion paper (McRobie(2013) arxiv:1304.3918), a simple set of `elemental' estimators was presented for the Generalized Pareto tail parameter. Each elemental estimator: involves only three log-spacings; is absolutely unbiased for all…
The estimation of conditional quantiles at extreme tails is of great interest in numerous applications. Various methods that integrate regression analysis with an extrapolation strategy derived from extreme value theory have been proposed…
We present a new method for estimating the edge of a two-dimensional bounded set, given a finite random set of points drawn from the interior. The estimator is based both on Haar series and extreme values of the point process. We give…
In a task where many similar inverse problems must be solved, evaluating costly simulations is impractical. Therefore, replacing the model $y$ with a surrogate model $y_s$ that can be evaluated quickly leads to a significant speedup. The…
Subspace methods are commonly used for finding approximate eigenvalues and singular values of large-scale matrices. Once a subspace is found, the Rayleigh-Ritz method (for symmetric eigenvalue problems) and Petrov-Galerkin projection (for…
Accurate computation of robust estimates for extremal quantiles of empirical distributions is an essential task for a wide range of applicative fields, including economic policymaking and the financial industry. Such estimates are…
We constuct a sequential adaptive procedure for estimating the autoregressive function at a given point in nonparametric autoregression models with Gaussian noise. We make use of the sequential kernel estimators. The optimal adaptive…