Related papers: Weak error for nested Multilevel Monte Carlo

While the Quasi-Monte Carlo method of numerical integration achieves smaller integration error than standard Monte Carlo, its use in particle physics phenomenology has been hindered by the abscence of a reliable way to estimate that error.…

We present novel Monte Carlo (MC) and multilevel Monte Carlo (MLMC) methods to determine the unbiased covariance of random variables using h-statistics. The advantage of this procedure lies in the unbiased construction of the estimator's…

Despite the simplicity and intuitive interpretation of Minimum Mean Squared Error (MMSE) estimators, their effectiveness in certain scenarios is questionable. Indeed, minimizing squared errors on average does not provide any form of…

Model selection (MS) and model averaging (MA) are two popular approaches when having many candidate models. Theoretically, the estimation risk of an oracle MA is not larger than that of an oracle MS because the former one is more flexible,…

In this article, we propose a space-time Multi-Index Monte Carlo (MIMC) estimator for a one-dimensional parabolic stochastic partial differential equation (SPDE) of Zakai type. We compare the complexity with the Multilevel Monte Carlo…

Consider the nonparametric regression model Y=m(X)+E, where the function m is smooth but unknown, and E is independent of X. An estimator of the density of the error term E is proposed and its weak consistency is obtained. The contribution…

The aim of this paper is to obtain mixed weak-type inequalities for multilinear fractional operators, extending results by F. Berra, M. Carena and G. Pradolini \cite{BCP}. We prove that, under certain conditions on the weights, there exists…

We study the use of the multilevel Monte Carlo technique in the context of the calculation of Greeks. The pathwise sensitivity analysis differentiates the path evolution and reduces the payoff's smoothness. This leads to new challenges: the…

In this paper, starting with a relatively simple observation that the variational estimates of the commutators of the standard Calder\'on-Zygmund operators with the BMO functions can be deduced from the weighted variational estimates of the…

Multi-fidelity Monte Carlo (MFMC) is a variance reduction method that leverages a multi-fidelity ensemble of models of varying cost and accuracy levels. Constructing an MFMC estimator with optimal variance requires knowledge of the…

Random field Monte Carlo (MC) reliability analysis is a robust stochastic method to determine the probability of failure. This method, however, requires a large number of numerical simulations demanding high computational costs. This paper…

In this paper, the authors establish some weighted estimates for the Calder\'on commutator defined by \begin{eqnarray*} &&\mathcal{C}_{m+1,\,A}(a_1,\dots,a_{m};f)(x) &&\quad={\rm…

A biomechanical model often requires parameter estimation and selection in a known but complicated nonlinear function. Motivated by observing that data from a head-neck position tracking system, one of biomechanical models, show…

We consider the problem of estimating an unknown function f* and its partial derivatives from a noisy data set of n observations, where we make no assumptions about f* except that it is smooth in the sense that it has square integrable…

Markov chain Monte Carlo (MCMC) produces a correlated sample for estimating expectations with respect to a target distribution. A fundamental question is when should sampling stop so that we have good estimates of the desired quantities?…

When solving stochastic partial differential equations (SPDEs) driven by additive spatial white noise, the efficient sampling of white noise realizations can be challenging. Here, we present a new sampling technique that can be used to…

Uncertainty quantification in a neural network is one of the most discussed topics for safety-critical applications. Though Neural Networks (NNs) have achieved state-of-the-art performance for many applications, they still provide…

This paper explores the estimation of a panel data model with cross-sectional interaction that is flexible both in its approach to specifying the network of connections between cross-sectional units, and in controlling for unobserved…

This paper analyzes the classical linear regression model with measurement errors in all the variables. First, we provide necessary and sufficient conditions for identification of the coefficients. We show that the coefficients are not…

Generalized additive partial linear models (GAPLMs) are appealing for model interpretation and prediction. However, for GAPLMs, the covariates and the degree of smoothing in the nonparametric parts are often difficult to determine in…