Related papers: Two-sided inequalities for the density function's …
This paper focuses on inhomogeneous quadratic tests, which involve the sum of a dependent non-central chi-square with a Gaussian random variable. Unfortunately, no closed-form expression is available for the statistical distribution of the…
We give a set of necessary conditions for locality in bipartite systems, which include and generalize known Bell's inequalities. Each condition corresponds to a specific order of the expansion of random variables defined on graphs, in terms…
In this paper we study sectional curvature bounds for Riemannian manifolds with density from the perspective of a weighted torsion free connection introduced recently by the last two authors. We develop two new tools for studying weighted…
We propose a construction of frequentist confidence intervals that is effective near unphysical regions and unifies the treatment of two-sided and upper limit intervals. It is rigorous, has coverage, is computationally simple and avoids the…
Critical points of a scalar quantitiy are either extremal points or saddle points. The character of the critical points is determined by the sign distribution of the eigenvalues of the Hessian matrix. For a two-dimensional homogeneous and…
The subject is the overview of the use of quasi-entropy in finite dimensional spaces. Matrix monotone functions and relative modular operators are used. The origin is the relative entropy and the f-divergence, monotone metrics, covariance…
We investigate the fine-grained uncertainty relations for qubit system by measurements corresponding respectively to two and three spin operators. Then we derive the general bound for a combination of two probabilities of projective…
The representation of integral binary forms as sums of two squares is discussed and applied to establish the Manin conjecture for certain Ch\^atelet surfaces defined over the rationals.
We develop a theory of limits of finite posets in close analogy to the recent theory of graph limits. In particular, we study representations of the limits by functions of two variables on a probability space, and connections to…
In this paper we show that the conditional distribution of perturbed chi-quare risks can be approximated by certain distributions including the Gaussian ones. Our results are of interest for conditional extreme value models and multivariate…
We investigate the statistics of stationary points in the sum of squares of $N$ Gaussian random fields, which we call a "chi-squared" field. The behavior of such a field at a point is investigated, with particular attention paid to the…
Chebyshev famously observed empirically that more often than not, there are more primes of the form $3 \bmod 4$ up to $x$ than of the form $1 \bmod 4$. This was confirmed theoretically much later by Rubinstein and Sarnak in a logarithmic…
A weighted game or a threshold function in general admits different weighted representations even if the sum of non-negative weights is fixed to one. Here we study bounds for the diameter of the corresponding weight polytope. It turns out…
In this paper, we derive new probability bounds for Chebyshev's inequality if the supremum of the probability density function is known. This result holds for one-dimensional or multivariate continuous probability distributions with finite…
Motivated by the likelihood ratio test under the Gaussian assumption, we develop a maximum sum-of-squares test for conducting hypothesis testing on high dimensional mean vector. The proposed test which incorporates the dependence among the…
We give a simple inequality for the sum of independent bounded random variables. This inequality improves on the celebrated result of Hoeffding in a special case. It is optimal in the limit where the sum tends to a Poisson random variable.
In order to quantify the error budget in the measured probability distribution functions of cell densities, the two-point statistics of cosmic densities in concentric spheres is investigated. Bias functions are introduced as the ratio of…
Data sets collected at different times and different observing points can possess correlations at different times $and$ at different positions. The doubly correlated Wishart model takes both into account. We calculate the eigenvalue density…
In the present paper new insights into the study of the Non-central Dirichlet distribution are provided. This latter is the analogue of the Dirichlet distribution obtained by replacing the Chi-Squared random variables involved in its…
We develop a unified nonparametric framework for sharp partial identification and inference on inequality indices when the data contain coarsened observations of the variable of interest. We characterize the extremal allocations for all…