Related papers: Refined normal approximations for the Student dist…
We present an extension of local sensitivity analysis, also referred to as the perturbation approach for uncertainty quantification, to Bayesian inverse problems. More precisely, we show how moments of random variables with respect to the…
For an unknown continuous distribution on a real line, we consider the approximate estimation by the discretization. There are two methods for the discretization. First method is to divide the real line into several intervals before taking…
We introduce the problem of variable-length source resolvability, where a given target probability distribution is approximated by encoding a variable-length uniform random number, and the asymptotically minimum average length rate of the…
This paper investigates the large sample properties of local regression distribution estimators, which include a class of boundary adaptive density estimators as a prime example. First, we establish a pointwise Gaussian large sample…
We establish the rate of convergence of distributions of sums of independent identically distributed random variables to the Gaussian distribution in terms of truncated pseudomoments by implementing the idea of Yu. Studnyev for getting…
We study the local limit theorem for weighted sums of Bernoulli variables. We show on examples that this is an important question in the general theory of the local limit theorem, and which turns up to be not well explored. The examples we…
We discuss in detail the asymptotic distribution of sample expectiles. First, we show uniform consistency under the assumption of a finite mean. In case of a finite second moment, we show that for expectiles other then the mean, only the…
We present a rather general method for proving local limit theorems, with a good rate of convergence, for sums of dependent random variables. The method is applicable when a Stein coupling can be exhibited. Our approach involves both…
Given a loss function $F:\mathcal{X} \rightarrow \R^+$ that can be written as the sum of losses over a large set of inputs $a_1,\ldots, a_n$, it is often desirable to approximate $F$ by subsampling the input points. Strong theoretical…
In this paper, we first establish general bounds on the Fisher information distance to the class of normal distributions of Malliavin differentiable random variables. We then study the rate of Fisher information convergence in the central…
We consider 1-dimensional location estimation, where we estimate a parameter $\lambda$ from $n$ samples $\lambda + \eta_i$, with each $\eta_i$ drawn i.i.d. from a known distribution $f$. For fixed $f$ the maximum-likelihood estimate (MLE)…
We establish both uniform and nonuniform error bounds of the Berry-Esseen type in normal approximation under local dependence. These results are of an order close to the best possible if not best possible. They are more general or sharper…
In this paper we give an explicit bound on the distance to chisquare for the likelihood ratio statistic when the data are realisations of independent and identically distributed random elements. To our knowledge this is the first explicit…
We derive distributional limits for empirical transport distances between probability measures supported on countable sets. Our approach is based on sensitivity analysis of optimal values of infinite dimensional mathematical programs and a…
In this paper we prove a quantiative local limit theorem for the distribution of the number of triangles in the Erd\H{o}s-Renyi random graph $G(n,p)$, for a fixed $p\in (0,1)$. This proof is an extension of the previous work of Gilmer and…
This paper studies probabilistic rates of convergence for consensus+innovations type of algorithms in random, generic networks. For each node, we find a lower and also a family of upper bounds on the large deviations rate function, thus…
We herein establish an asymptotic representation theorem for locally asymptotically normal quantum statistical models. This theorem enables us to study the asymptotic efficiency of quantum estimators such as quantum regular estimators and…
The beta normal distribution is a generalization of both the normal distribution and the normal order statistics. Some of its mathematical properties and a few applications have been studied in the literature. We provide a better foundation…
We study the empirical likelihood approach to construct confidence intervals for the optimal value and the optimality gap of a given solution, henceforth quantify the statistical uncertainty of sample average approximation, for optimization…
In a remarkable paper, Peter Hall [{\it On the rate of convergence of normal extremes}, J. App. Prob, {\bf 16} (1979) 433--439] proved that the supremum norm distance between the distribution function of the normalized maximum of $n$…