Related papers: A note on optimal probability lower bounds for cen…

In this note we would like to give an explicit lower bound by using a lower saturated subset of \mathbb{R}_{\geq 0}^n.

The paper presents two results. The first one provides separate conditions for the upper and lower estimate of the distribution of the exit time from balls of a random walk on a weighted graph. The main result of the paper is that the lower…

Consider the problem of maximizing the probability of stopping with one of the two highest values in a Bernoulli random walk with arbitrary parameter $p$ and finite time horizon $n$. Allaart \cite{Allaart} proved that the optimal strategy…

Consider a remote estimation problem where a sensor wants to communicate the state of an uncertain source to a remote estimator over a finite time horizon. The uncertain source is modeled as an autoregressive process with bounded noise.…

We present the first minimax risk bounds for estimators of the spectral measure in multivariate linear factor models, where observations are linear combinations of regularly varying latent factors. Non-asymptotic convergence rates are…

This paper considers a distributionally robust chance constraint model with a general ambiguity set. We show that a sample based approximation of this model converges under suitable sufficient conditions. We also show that upper and lower…

We propose two families of asymptotically local minimax lower bounds on parameter estimation performance. The first family of bounds applies to any convex, symmetric loss function that depends solely on the difference between the estimate…

The term moderate deviations is often used in the literature to mean a class of large deviation principles that, in some sense, fills the gap between a convergence in probability of some random variables to a constant and a weak convergence…

The approximation of a discrete probability distribution $\mathbf{t}$ by an $M$-type distribution $\mathbf{p}$ is considered. The approximation error is measured by the informational divergence $\mathbb{D}(\mathbf{t}\Vert\mathbf{p})$, which…

We derive conditions under which random sequences of polarizations (two-point symmetrizations) converge almost surely to the symmetric decreasing rearrangement. The parameters for the polarizations are independent random variables whose…

Many discrete-time optimal stopping problems are known to have more tractable limit forms based on a planar Poisson process. Using this tool we find a solution to the optimal stopping problem for i.i.d. sequence of $n$ discrete uniform…

We investigate the high-probability estimation of discrete distributions from an \iid sample under $\chi^2$-divergence loss. Although the minimax risk in expectation is well understood, its high-probability counterpart remains largely…

We calculate the p-the moment of the sum of n independent random variables with respect to symmetric norm in R^n. The order of growth for upper bound p/ln p obtained in ths estimate is optimal. The result extends to generalized Lorentz…

Prediction sets can wrap around any ML model to cover unknown test outcomes with a guaranteed probability. Yet, it remains unclear how to use them optimally for downstream decision-making. Here, we propose a decision-theoretic framework…

In this paper we construct optimal, in certain sense, estimates of values of linear functionals on solutions to two-point boundary value problems (BVPs) for systems of linear first-order ordinary differential equations from observations…

Let S_n:=a_1\vp_1+...+a_n\vp_n, where \vp_1,...,\vp_n are independent Rademacher random variables (r.v.'s) and a_1,...,a_n are any real numbers such that a_1^2+...+a_n^2=1. Let Z be a standard normal r.v. It is proved that the best constant…

In this work, we study the normal approximation and almost sure central limit theorems for some functionals of an independent sequence of Rademacher random variables. In particular, we provide a new chain rule that improves the one derived…

We present a coupled decreasing sequence of random walks on $ \mathbb Z $ that dominates the edge process of oriented-bond percolation in two dimensions. Using the concept of "random walk in a strip ", we construct an algorithm that…

A certain spectrum, indexed by a\in[0,\infty], of upper bounds P_a(X;x) on the tail probability P(X\geq x), with P_0(X;x)=P(X\geq x) and P_\infty(X;x) being the best possible exponential upper bound on P(X\geq x), is shown to be stable and…

In the paper "The best m-term approximation and greedy algorithms" (V. N. Temlyakov), an error bound for a near best m-term approximation of a function g in L^p([0,1]^d) is provided, using a basis L^p-equivalent to the Haar system, where p…