Related papers: Tight Bounds for Local Glivenko-Cantelli
Quantile aggregation with dependence uncertainty has a long history in probability theory with wide applications in finance, risk management, statistics, and operations research. Using a recent result on inf-convolution of quantile-based…
We develop a new formulation of Stein's method to obtain computable upper bounds on the total variation distance between the geometric distribution and a distribution of interest. Our framework reduces the problem to the construction of a…
We derive concentration inequalities for the supremum norm of the difference between a kernel density estimator (KDE) and its point-wise expectation that hold uniformly over the selection of the bandwidth and under weaker conditions on the…
We consider a classical model related to an empirical distribution function $ F_n(t)=\frac{1}{n}\sum_{k=1}^nI_{\{\xi_k\le t\}}$ of $(\xi_k)_{i\ge 1}$ -- i.i.d. sequence of random variables, supported on the interval $[0,1]$, with continuous…
We derive a general upper bound for the number of incidences with $k$-dimensional varieties in ${\mathbb R}^d$. The leading term of this new bound generalizes previous bounds for the special cases of $k=1, k=d-1,$ and $k= d/2$, to every…
We explore asymptotically optimal bounds for deviations of Bernoulli convolutions from the Poisson limit in terms of the Shannon relative entropy and the Pearson $\chi^2$-distance. The results are based on proper non-uniform estimates for…
We explore asymptotically optimal bounds for deviations of distributions of independent Bernoulli random variables from the Poisson limit in terms of the Shannon relative entropy and R\'enyi/Tsallis relative distances (including Pearson's…
The Kolmogorov-Smirnov statistic is usually introduced as a supremum, but its finite-sample behavior is governed by a more local question: where does the empirical process first cross a boundary? This letter gives a partial answer through a…
We investigate the problem of semi-parametric maximum likelihood under constraints on summary statistics. Such a procedure results in a discrete probability distribution that maximises the likelihood among all such distributions under the…
We derive the exponential non improvable Grand Lebesgue Space norm decreasing estimations for tail of distribution for exact normed deviation for the famous recursive Wolverton-Wagner multivariate statistical density estimation. We consider…
We obtain explicit error bounds for the $d$-dimensional normal approximation on hyperrectangles for a random vector that has a Stein kernel, or admits an exchangeable pair coupling, or is a non-linear statistic of independent random…
A Chernoff-type distribution is a nonnormal distribution defined by the slope at zero of the greatest convex minorant of a two-sided Brownian motion with a polynomial drift. While a Chernoff-type distribution is known to appear as the…
Consider the task of generating samples from a tilted distribution of a random vector whose underlying distribution is unknown, but samples from it are available. This finds applications in fields such as finance and climate science, and in…
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…
Many causal and structural parameters in economics can be identified and estimated by computing the value of an optimization program over all distributions consistent with the model and the data. Existing tools apply when the data is…
The likelihood function of a finite mixture model is a non-convex function with multiple local maxima and commonly used iterative algorithms such as EM will converge to different solutions depending on initial conditions. In this paper we…
We establish effective convergence rates in the Doeblin-Lenstra law, describing the limiting distribution of approximation coefficients arising from continued fraction convergents of a typical real number. More generally, we prove…
This paper investigates a local central limit theorem for a normalized sequence of random variables belonging to a fixed order Wiener chaos and converging to the standard normal distribution. We prove, without imposing any additional…
We develop a Glivenko--Cantelli theory for monotone, almost additive functions of i.\,i.\,d.\ sequences of random variables indexed by~$\Z^d$. Under certain conditions on the random sequence, short range correlations are allowed as well. We…
This paper derives new bounds on the difference of the entropies of two discrete random variables in terms of the local and total variation distances between their probability mass functions. The derivation of the bounds relies on maximal…