Related papers: Multivariate Chebyshev Inequality with Estimated M…
We study admissibility of a subclass of generalized Bayes estimators of a multivariate normal vector when the variance is unknown, under scaled quadratic loss. Minimaxity is also established for certain of these estimators.
Based on collection of bijections, variable and function are extended into ``isomorphic variable'' and ``dual-variable-isomorphic function'', then mean values such as arithmetic mean and mean of a function are extended to ``isomorphic…
We show that any weighted geometric mean of Chebyshev polynomials is bounded from above by another Chebyshev polynomial. We also study a related homogeneous cyclic inequality $$ \left (\sum_{i=1}^n x_i^{(a+b+1)/2} \right )^2 \geq…
Gau\ss (1823) proved a sharp upper bound on the probability that a random variable falls outside a symmetric interval around zero when its distribution is unimodal with mode at zero. For the class of all distributions with mean at zero,…
The Bell inequality constrains the outcomes of measurements on pairs of distant entangled particles. The Bell contradiction states that the Bell inequality is inconsistent with the calculated outcomes of these quantum experiments. This…
In this paper we propose an optimal predictor of a random variable that has either an infinite mean or an infinite variance. The method consists of transforming the random variable such that the transformed variable has a finite mean and…
The aim of this paper is to study, in the infinite dimensional framework, the existence and uniqueness for the solution of the following multivalued generalized backward stochastic differential equation, considered on a random, possibly…
In this paper we give an explicit bound on the distance to chisquare for the likelihood ratio statistic when the data are realisations of independent and identically distributed random elements. To our knowledge this is the first explicit…
We study the problem of estimating the mean of a multivariatedistribution based on independent samples. The main result is the proof of existence of an estimator with a non-asymptotic sub-Gaussian performance for all distributions…
We prove a Chernoff-type upper variance bound for the multinomial and the negative multinomial distribution. An application is also given.
We derive simple concentration inequalities for bounded random vectors, which generalize Hoeffding's inequalities for bounded scalar random variables. As applications, we apply the general results to multinomial and Dirichlet distributions…
A general formula is presented for any order derivative of Chebyshev polynomials instead of the existing recursive relationship. Hence, the Chebyshev finite difference method is made applicable not only to second order problems but also to…
The work concerns invariant measures for multivalued McKean-Vlasov stochastic differential equations. First of all, we prove the exponential ergodicity of these equations. Then for a sequence of these equations, when their coefficients…
The question of testing for equality in distribution between two linear models, each consisting of sums of distinct discrete independent random variables with unequal numbers of observations, has emerged from the biological research. In…
We show somewhat unexpectedly that whenever a general Bernstein-type maximal inequality holds for partial sums of a sequence of random variables, a maximal form of the inequality is also valid.
We extend a general Bernstein-type maximal inequality of Kevei and Mason (2011) for sums of random variables.
We introduce methods to bound the mean of a discrete distribution (or finite population) based on sample data, for random variables with a known set of possible values. In particular, the methods can be applied to categorical data with…
The sample mean is often used to aggregate different unbiased estimates of a parameter, producing a final estimate that is unbiased but possibly high-variance. This paper introduces the Bayesian median of means, an aggregation rule that…
This paper proposes a Bayesian method for estimating the parameters of a normal distribution when only limited summary statistics (sample mean, minimum, maximum, and sample size) are available. To estimate the parameters of a normal…
Two--sided bounds are constructed for a probability density function of a weighted sum of chi-square variables. Both cases of central and non-central chi-square variables are considered. The upper and lower bounds have the same dependence…