Related papers: Quasi-Hadamard differentiability of general risk f…
The functional delta-method provides a convenient tool for deriving bootstrap consistency of a sequence of plug-in estimators w.r.t. a given functional from bootstrap consistency of the underlying sequence of estimators. It has recently…
The functional delta-method provides a convenient tool for deriving the asymptotic distribution of a plug-in estimator of a statistical functional from the asymptotic distribution of the respective empirical process. Moreover, it provides a…
In this paper, we develop a functional differentiability approach for solving statistical optimal allocation problems. We derive Hadamard differentiability of the value functions through analyzing the properties of the sorting operator…
We study boundary values of harmonic functions in spaces of quasianalytic functionals and spaces of ultradistributions of non-quasianalytic type. As an application, we provide a new approach to H\"ormander's support theorem for…
We show that various functionals related to the supremum of a real function defined on an arbitrary set or a measure space are Hadamard directionally differentiable. We specifically consider the supremum norm, the supremum, the infimum, and…
It is commonly acknowledged that V-functionals with an unbounded kernel are not Hadamard differentiable and that therefore the asymptotic distribution of U- and V-statistics with an unbounded kernel cannot be derived by the Functional Delta…
In this paper, the asymptotic distributions of estimators for the regularized functional canonical correlation and variates of the population are derived. The method is based on the possibility of expressing these regularized quantities as…
In this article, we present a nonparametric method for the general two-sample problem involving functional random variables modelled as elements of a separable Hilbert space ${\cal H}$. First, we present a general recipe based on linear…
$f$-divergences, which quantify discrepancy between probability distributions, are ubiquitous in information theory, machine learning, and statistics. While there are numerous methods for estimating $f$-divergences from data, a limit…
Motivated by the problem of the dynamics of point-particles in high post-Newtonian (e.g. 3PN) approximations of general relativity, we consider a certain class of functions which are smooth except at some isolated points around which they…
This paper studies an asymptotic framework for conducting inference on parameters of the form $\phi(\theta_0)$, where $\phi$ is a known directionally differentiable function and $\theta_0$ is estimated by $\hat \theta_n$. In these settings,…
We consider the copula mapping, which maps a joint cumulative distribution function to the corresponding copula. Its Hadamard differentiablity was shown in van der Vaart and Wellner (1996), Fermanian et al. (2004) and (under less strict…
We develop a non-standard analysis framework for coherent risk measures and their finite-sample analogues, coherent risk estimators, building on recent work of Aichele, Cialenco, Jelito, and Pitera. Coherent risk measures on $L^\infty$ are…
The functional delta-method has a wide range of applications in statistics. Applications on functionals of empirical processes yield various limit results for classical statistics. To improve the finite sample properties of statistical…
In this paper we show several connections between special functions arising from generalized COM-Poisson-type statistical distributions and integro-differential equations with varying coefficients involving Hadamard-type operators. New…
The delta method is a popular and elementary tool for deriving limiting distributions of transformed statistics, while applications of asymptotic distributions do not allow one to obtain desirable accuracy of approximation for tail…
We address the statistical estimation of composite functionals which may be nonlinear in the probability measure. Our study is motivated by the need to estimate coherent measures of risk, which become increasingly popular in finance,…
Density-corrected density functional theory (DC-DFT) is enjoying substantial success in improving semilocal DFT calculations in a wide variety of chemical problems. This paper provides the formal theoretical framework and assumptions for…
This paper develops asymptotic theory of integrals of empirical quantile functions with respect to random weight functions, which is an extension of classical $L$-statistics. They appear when sample trimming or Winsorization is applied to…
Many different types of fractional calculus have been defined, which may be categorised into broad classes according to their properties and behaviours. Two types that have been much studied in the literature are the Hadamard-type…