Related papers: On the Impact of Approximation Errors on Extreme Q…
We derive a priori error estimates for Nitsche's method applied to elliptic problems on approximate domains. Such approximations arise, for example, in unfitted finite element methods, data-driven simulations, and evolving domain problems,…
Asymptotic normality of extreme value tail estimators received much attention in the literature, giving rise to increasingly complicated 2nd order regularity conditions. However, such conditions are really difficult to be checked for real…
The new ingredient of this paper is that we consider infinitely dimensional classes of functions and instead of the relative error setting, which was used in previous papers on norm discretization, we consider the absolute error setting. We…
Strong approximation errors of both finite element semi-discretization and spatio-temporal full discretization are analyzed for the stochastic Allen-Cahn equation driven by additive noise in space dimension $d \leq 3$. The full…
This paper introduces an upper bound on the absolute difference between: (a) the cumulative distribution function (CDF) of the sum of a finite number of independent and identically distributed random variables with finite absolute third…
Estimating the tail index parameter is one of the primal objectives in extreme value theory. For heavy-tailed distributions the Hill estimator is the most popular way to estimate the tail index parameter. Improving the Hill estimator was…
It is a typical standard assumption in the density deconvolution problem that the characteristic function of the measurement error distribution is non-zero on the real line. While this condition is assumed in the majority of existing works…
In several different fields, there is interest in analyzing the upper or lower tail quantile of the underlying distribution rather than mean or center quantile. However, the investigation of the tail quantile is difficult because of data…
We extend the classical Heisenberg uncertainty principle to a fractional $L^p$ setting by investigating a novel class of uncertainty inequalities derived from the fractional Schr\"odinger equation. In this work, we establish the existence…
We consider infinitely dimensional classes of functions and instead of the relative error setting, which was used in previous papers on the integral norm discretization, we consider the absolute error setting. We demonstrate how known…
Estimation of tail quantities, such as expected shortfall or Value at Risk, is a difficult problem. We show how the theory of nonlinear expectations, in particular the Data-robust expectation introduced in [5], can assist in the…
In this paper we consider the semi-parametric estimation of extreme quantiles of a right heavy-tail model. We propose a new Log Probability Weighted Moment estimator for extreme quantiles, which is obtained from the estimators of the shape…
We consider upper bounds for the approximation error E|g(X)-g(\hat X)|^p, where X and \hat X are random variables such that \hat X is an approximation of X in the L_p-norm, and the function g belongs to certain function classes, which…
Many management decisions involve accumulated random realizations for which only the first and second moments of their distribution are available. The sharp Chebyshev-type bound for the tail probability and Scarf bound for the expected loss…
A class of causal effect functionals requires integration over conditional densities of continuous variables, as in mediation effects and nonparametric identification in causal graphical models. Estimating such densities and evaluating the…
This paper addresses the problem of estimating, in the presence of random censoring as well as competing risks, the extreme value index of the (sub)-distribution function associated to one particular cause, in the heavy-tail case.…
This paper concerns estimation and inference for treatment effects in deep tails of the counterfactual distribution of unobservable potential outcomes corresponding to a continuously valued treatment. We consider two measures for the deep…
In this paper, we revisit approximation properties of piecewise polynomial spaces, which contain more than ${\cal P}_{r-1}$ but not ${\cal P}_r$. We develop more accurate upper and lower error bounds that are sharper than those used in…
Standard statistical analysis is unable to provide reliable confidence intervals on expectation values of probability distributions that do not satisfy the conditions of the central limit theorem. We present a regression-based estimator of…
The first order loss function and its complementary function are extensively used in practical settings. When the random variable of interest is normally distributed, the first order loss function can be easily expressed in terms of the…