Related papers: Moment Inequalities for Symmetric Statistics
We establish new functional versions of the Blaschke-Santal\'o inequality on the volume product of a convex body which generalize to the non-symmetric setting an inequality of K. Ball and we give a simple proof of the case of equality. As a…
Let E be a separable (or the dual of a separable) symmetric function space, let M be a semifinite von Neumann algebra and let E(M) be the associated noncommutative function space. Let $(\epsilon_k)_k$ be a Rademacher sequence, on some…
We collect in this note some observations on the role of symmetries in Bayesian inference problems, that can be useful or detrimental depending on the way they act on the signal and on the observations. We emphasize in particular the need…
The inequality between rank and crank moments was conjectured and later proved by Garvan himself in 2011. Recently, Dixit and the authors introduced finite analogues of rank and crank moments for vector partitions while deriving a finite…
In this paper we improve a result on the order of magnitude of certain cotangent sums associated to the Estermann and the Riemann zeta functions.
We introduce the Statistical Asynchronous Regression (SAR) method: a technique for determining a relationship between two time varying quantities without simultaneous measurements of both quantities. We require that there is a time…
A common experimental strategy for demonstrating non-classical correlations is to show violation of a Bell inequality by measuring a continuously emitted stream of entangled photon pairs. The measurements involve the detection of photons by…
We establish formulae for the moments of the moments of the characteristic polynomials of random orthogonal and symplectic matrices in terms of certain lattice point count problems. This allows us to establish asymptotic formulae when the…
We calculate asymptotic expansions for the moments of number of comparisons used by the randomized quick sort algorithm using the singularity analysis of certain generating functions.
The position-momentum uncertainty-like inequality based on moments of arbitrary order for d-dimensional quantum systems, which is a generalization of the celebrated Heisenberg formulation of the uncertainty principle, is improved here by…
Counterfactuals in quantum theory are briefly reviewed and it is argued that they are very different from counterfactuals considered in the general philosophical literature. The issue of time symmetry of quantum counterfactuals is…
Properties satisfied by the moments of the partial non-central chi-square distribution function, also known as Nuttall Q-functions, and methods for computing these moments are discussed in this paper. The Nuttall Q-function is involved in…
We propose a simple test for moment inequalities that has exact size in normal models with known variance and has uniformly asymptotically exact size more generally. The test compares the quasi-likelihood ratio statistic to a chi-squared…
We consider random matrices that have invariance properties under the action of unitary groups (either a left-right invariance, or a conjugacy invariance), and we give formulas for moments in terms of functions of eigenvalues. Our main tool…
This note uses a simple example to show how moment inequality models used in the empirical economics literature lead to general minimax relative efficiency comparisons. The main point is that such models involve inference on a low…
Time reversal symmetric triangular maps of the unit square are introduced with the property that the time evolution of one of their two variables is determined by a piecewise expanding map of the unit interval. We study their statistical…
We refine Khintchine Transference Principle which relates the measure of simultaneous rational approximation of an $n$ real numbers with the measure of linear independence of these $n$ numbers. Khintchine's inequalities are known to be…
We revisit the method of Kirschenhofer, Prodinger and Tichy to calculate the moments of comparisons used by the quick sort algorithm. We reemphasize that this approach helps in calculating these quantities with less computation. We also…
We establish concentration inequalities for random dynamical systems (RDSs), assuming that the observables of interest are separately Lipschitz. Under a weak average contraction condition, we obtain deviation bounds for several random…
In this paper we prove the S-inequality for certain product probability measures and ideals in R^n . As a result, for the Weibull and Gamma product distributions we derive concentration of measure type estimates as well as optimal…