Equivalent Conditions of Complete p th Moment Convergence for Weighted Sums of I. I. D. Random Variables under Sublinear Expectations

We investigate the complete p th moment convergence for weighted sums of independent, identically distributed random variables under sublinear expectations space. Using moment inequality and truncation methods, we prove the equivalent conditions of complete p th moment convergence of weighted sums of independent, identically distributed random variables under sublinear expectations space, which complement the corresponding results obtained in Guo and Shan (2020).

Testing brnbu ageing class of life-time distribution based on moment inequality

In this paper, new moment inequality is derived for Bivariate Renewal New Better than Used (BRNBU) ageing class of life-time distribution. This inequality demonstrates that if the mean life is finite, then all higher order moments exist. Based on the Moment inequality, new testing procedures for testing bivariate exponentiality against BRNBU ageing class of life-time distribution is introduced.The asymptotic normality of the test statistic and its consistency are studied. Using Monte Carlo Method, critical values of the proposed test are calculated for n= 5(5)100 and tabulated. Finally, the theoretical results are applied to analyze real-life data sets.

Computing moment inequality models using constrained optimization

Inference for moment inequality models is computationally demanding and often involves time-consuming grid search. By exploiting the equivalent formulations between unconstrained and constrained optimization, we establish new ways to compute the identified set and its confidence set in moment inequality models which overcome some of these computational hurdles. In simulations, using both linear and nonlinear moment inequality models, we show that our method significantly improves the solution quality and save considerable computing resources relative to conventional grid search. Our methods are user-friendly and can be implemented using a variety of canned software packages.

Strong Limit Theorems for Dependent Random Variables

In this article We establish moment inequality of dependent random variables, furthermore some theorems of strong law of large numbers and complete convergence for sequences of dependent random variables. In particular, independent and identically distributed Marcinkiewicz Law of large numbers are generalized to the case of m₀ -dependent sequences.

A Two-Moment Inequality with Applications to Rényi Entropy and Mutual Information

This paper explores some applications of a two-moment inequality for the integral of the rth power of a function, where 0<r<1. The first contribution is an upper bound on the Rényi entropy of a random vector in terms of the two different moments. When one of the moments is the zeroth moment, these bounds recover previous results based on maximum entropy distributions under a single moment constraint. More generally, evaluation of the bound with two carefully chosen nonzero moments can lead to significant improvements with a modest increase in complexity. The second contribution is a method for upper bounding mutual information in terms of certain integrals with respect to the variance of the conditional density. The bounds have a number of useful properties arising from the connection with variance decompositions.