Related papers: Maximizing the expected range from dependent obser…

For functions of independent random variables, various upper and lower variance bounds are revisited in diverse settings. These are then specialized to the Bernoulli, Gaussian, infinitely divisible cases and to Banach space valued random…

In this paper, we derive generic bounds on the maximum deviations in prediction errors for sequential prediction via an information-theoretic approach. The fundamental bounds are shown to depend only on the conditional entropy of the data…

Let $X$ denote a nonnegative random variable with $\mathsf{E} X<\infty$. Upper and lower bounds on $\mathsf{E} X-\exp\mathsf{E}\ln X$ are obtained, which are exact, in terms of $V_X$ and $E_X$ for the upper bound and in terms of $V_X$ and…

In this paper, tight upper and lower bounds are derived on the weighted sum of minimum mean-squared errors for additive Gaussian noise channels. The bounds are obtained by constraining the input distribution to be close to a Gaussian…

We study the maximum of the random assignment process on rectangular matrices. We derive first-order asymptotics for the expected maximum, prove a law of large numbers under mild tail assumptions, and obtain exponential upper bounds for the…

We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…

For a bivariate random vector (X,Y), symmetry conditions are presented that yield stochastic orderings among |X|, |Y|, |max(X,Y)|, and | min(X, Y)|. Partial extensions of these results for multivariate random vectors (X1,...,Xn) are also…

Let $\{X_{k,i};i\geq 1,k\geq 1\}$ be an array of i.i.d. random variables and let $\{p_n;n\geq 1\}$ be a sequence of positive integers such that $n/p_n$ is bounded away from 0 and $\infty$. For $W_n=\max_{1\leq i<j\leq…

A common statistical situation concerns inferring an unknown distribution Q(x) from a known distribution P(y), where X (dimension n), and Y (dimension m) have a known functional relationship. Most commonly, n<m, and the task is relatively…

We utilize quantum superposition principle to establish the improvable upper and lower bounds on the stronger uncertainty relation, i.e., the "weighted-like" sum of the variances of observables. Our bounds include some free parameters which…

The concept of univariate Range Value-at-Risk, presented by Cont et al. (2010), is extended in the multidimensional setting. Traditional risk measures are not well suited when dealing with heavy-tail distributions and infinite tail…

In classical extreme value theory probabilities of extreme events are estimated assuming all the components of a random vector to be in a domain of attraction of an extreme value distribution. In contrast, the conditional extreme value…

It is well known that the entropy $H(X)$ of a discrete random variable $X$ is always greater than or equal to the entropy $H(f(X))$ of a function $f$ of $X$, with equality if and only if $f$ is one-to-one. In this paper, we give tight…

Let X_1,X_2,... be a sequence of [0,1]-valued i.i.d. random variables, let c\geq 0 be a sampling cost for each observation and let Y_i=X_i-ic, i=1,2,.... For n=1,2,..., let M(Y_1,...,Y_n)=E(max_{1\leq i\leq n}Y_i) and…

We study the statistical limits of testing and estimation for a rank one deformation of a Gaussian random tensor. We compute the sharp thresholds for hypothesis testing and estimation by maximum likelihood and show that they are the same.…

The aim of this paper is to provide several novel upper bounds on the excess risk with a primal focus on classification problems. We suggest two approaches and the obtained bounds are represented via the distribution dependent local…

Variational approaches based on neural networks are showing promise for estimating mutual information (MI) between high dimensional variables. However, they can be difficult to use in practice due to poorly understood bias/variance…

Recursive max-linear vectors model causal dependence between its components by expressing each node variable as a max-linear function of its parental nodes in a directed acyclic graph and some exogenous innovation. Motivated by extreme…

In this paper a numerical method is presented, which finds a lower bound for the mutual information between a binary and an arbitrary finite random variable with joint distributions that have a variational distance not greater than a known…

Graphical models with bi-directed edges (<->) represent marginal independence: the absence of an edge between two vertices indicates that the corresponding variables are marginally independent. In this paper, we consider maximum likelihood…