Related papers: An Optimal Two Parameter Bounds for the Identric M…
We continue the study of how one can define means of infinite sets. We introduce many new properties, investigate their relations to each other and how they can typify a mean. We collect the properties in property groups e.g. for…
An exact upper bound on the Winsorised-tilted mean of a symmetric random variable in terms of its second moment is given. Such results are used in work on nonuniform Berry--Esseen-type bounds for general nonlinear statistics.
We obtain, in local coordinates, the explicit form of the two-dimensional, super-integrable systems of Matveev and Shevchishin involving cubic integrals. This enables us to determine for which values of the parameters these systems are…
We present a generalization of the maximal inequalities that upper bound the expectation of the maximum of $n$ jointly distributed random variables. We control the expectation of a randomly selected random variable from $n$ jointly…
Binary cyclic codes have been a hot topic for many years, and significant progress has been made in the study of this types of codes. As is well known, it is hard to construct infinite families of binary cyclic codes [n, n+1/2] with good…
We review a finite-sampling exponential bound due to Serfling and discuss related exponential bounds for the hypergeometric distribution. We then discuss how such bounds motivate some new results for two-sample empirical processes. Our…
The subject of this work is two treatment groups random coefficient regression models, in which observational units receive some group-specific treatments. We provide A- and D-optimality criteria for the estimation of the fixed parameter…
We propose a two-sample extended empirical likelihood for inference on the difference between two p-dimensional parameters defined by estimating equations. The standard two-sample empirical likelihood for the difference is Bartlett…
Recently, Gilmer proved the first constant lower bound for the union-closed sets conjecture via an information-theoretic argument. The heart of the argument is an entropic inequality involving the OR function of two i.i.d.\ binary vectors,…
We propose easily verifiable necessary and sufficient conditions for the linearizability of two-input systems by an endogenous dynamic feedback with a dimension of at most two.
The aim of this paper is to obtain new inequalities for a large family of generalizations of the Wiener Index and to characterize the set of extremal graphs with respect to them. Our main results provide upper and lower bounds for these…
We introduce a new approach for establishing fixed-parameter tractability of problems parameterized above tight lower bounds. To illustrate the approach we consider three problems of this type of unknown complexity that were introduced by…
In this review we cover the basics of efficient nonparametric parameter estimation (also called functional estimation), with a focus on parameters that arise in causal inference problems. We review both efficiency bounds (i.e., what is the…
We obtain sharp lower and upper bounds for the number of maximal (under inclusion) independent sets in trees with fixed number of vertices and diameter. All extremal trees are described up to isomorphism.
Combining a modular approach to the $abc$ conjecture developed by the second author with the classical method of linear forms in logarithms, we obtain improved unconditional bounds for two classical problems. First, for Szpiro's conjecture…
In this article, we address endpoint issues for the bilinear spherical maximal functions. We obtain borderline restricted weak type estimates for the well studied bilinear spherical maximal function…
We derive an optimal entropic uncertainty relation for an arbitrary pair of observables in a two-dimensional Hilbert space. Such a result, for the simple case we are considering, definitively improves all the entropic uncertainty relations…
In this paper, we give upper and lower bounds for the spectral radius of a nonnegative irreducible matrix and characterize the equality cases. These bounds theoretically improve and generalize some known results of Duan et al.[X. Duan, B.…
The paper derives the theoretical Cramer-Rao lower bound for parameter estimation of a source (of emitting energy, gas, aerosol), monitored by a network of sensors providing binary measurements. The theoretical bound is studied in the…
We present an extensive analysis of relative deviation bounds, including detailed proofs of two-sided inequalities and their implications. We also give detailed proofs of two-sided generalization bounds that hold in the general case of…