Related papers: Sharp bounds for cumulative distribution functions
We establish good numerical estimates for a certain class of integrals involving sixfold products of Bessel functions. We use relatively elementary methods. The estimates will be used in the study of a sharp Fourier restriction inequality…
The generalized Marcum functions appear in problems of technical and scientific areas such as, for example, radar detection and communications. In mathematical statistics and probability theory these functions are called the noncentral…
This paper deals with the problem of outliers in high frequency observation data from diffusion processes. Robust estimation methods are needed because the inclusion of outliers can lead to incorrect statistical inference even in the…
We establish explicit, universal, and distribution-free bounds for the $n$-th cumulant, $\kappa_n(X)$, of a scalar random variable, controlled solely by an $n$-th order absolute moment functional $M_n(X)$. The bounds take the form…
The problem of establishing out-of-sample bounds for the values of an unkonwn ground-truth function is considered. Kernels and their associated Hilbert spaces are the main formalism employed herein along with an observational model where…
Many enumeration problems in combinatorics, including such fundamental questions as the number of regular graphs, can be expressed as high-dimensional complex integrals. Motivated by the need for a systematic study of the asymptotic…
Let $X_1,X_2,...,X_n$ be a sequence of independent or locally dependent random variables taking values in $\mathbb{Z}_+$. In this paper, we derive sharp bounds, via a new probabilistic method, for the total variation distance between the…
In randomized trials, once the total effect of the intervention has been estimated, it is often of interest to explore mechanistic effects through mediators along the causal pathway between the randomized treatment and the outcome. In the…
We study the convergence of probability measures in terms of moments by applying operators to their Bessel generating functions. We consider a general setting of applying operators such as the Dunkl operator to formal power series that are…
We give a general method to obtain from the integral restrictions of functions sharp pointwise and uniform estimates of these functions. This scheme is illustrated by the examples for Fock\,--\,Bargmann spaces of entire functions of several…
We establish the limiting distribution of $\frac{{(\log \log x)}^{1/4}}{\sqrt{x}} \sum_{n\le x}\alpha(n)$ where $\alpha$ is a Steinhaus random multiplicative function, answering a question of Harper. The distributional convergence is proved…
An optimal bound on the quantiles of a certain kind of distributions is given. Such a bound is used in applications to Berry--Esseen-type bounds for nonlinear statistics.
The modified Bessel function of the first kind, $I_{\nu}(x)$, arises in numerous areas of study, such as physics, signal processing, probability, statistics, etc. As such, there has been much interest in recent years in deducing properties…
Spectral properties of Gram matrices are central to high dimensional asymptotic analyses of statistical estimators in regression and covariance estimation. These properties, in turn, depend critically on the extreme singular values and…
Quantitative formulations of Fefferman's counterexample for the ball multiplier are naturally linked to square function and vector-valued estimates for directional singular integrals. The latter are usually referred to as Meyer-type lemmas…
We obtain a Bernstein type Gaussian concentration inequality for martingales. Our inequality improves the Azuma-Hoeffding inequality for moderate deviations $x$. Following the work of McDiarmid (1989), Talagrand (1996) and Boucheron, Lugosi…
In this paper we consider the asymptotic distributions of functionals of the sample covariance matrix and the sample mean vector obtained under the assumption that the matrix of observations has a matrix-variate location mixture of normal…
We establish sharp estimates for the convergence rate of the Kranosel'ski\v{\i}-Mann fixed point iteration in general normed spaces, and we use them to show that the asymptotic regularity bound recently proved in [11] (Israel Journal of…
We consider three classes of linear differential equations on distribution functions, with a fractional order $\alpha\in [0,1].$ The integer case $\alpha =1$ corresponds to the three classical extreme families. In general, we show that…
An extension of the empirical copula is considered by combining an estimator of a multivariate cumulative distribution function with estimators of the marginal cumulative distribution functions for marginal estimators that are not…