In most situations the best estimator of a function of the parameter exists, but sometimes it has a complex form and we cannot compute its variance explicitly. Therefore, a lower bound for the variance of an estimator is one of the fundamentals in the estimation theory, because it gives us an idea about the accuracy of an estimator. It is well-known in statistical inference that the Cram&eac...

The paper furthers the neoclassical theory of earnings inequality. The inequality multiplier is derived as the amount by which inequality in skills must be multiplied to yield earnings inequality. Neutral technological change and the real interest rate affect inequality by changing capital per worker. The effect of capital per worker on the inequality multiplier is related to skill differential...

Abstract: An affine Moser-Trudinger inequality, which is stronger than the Euclidean MoserTrudinger inequality, is established. In this new affine analytic inequality an affine energy of the gradient replaces the standard L energy of gradient. The geometric inequality at the core of the affine Moser-Trudinger inequality is a recently established affine isoperimetric inequality for convex bodies...

This study performs a long-run, inter-temporal analysis of income inequality in the U.S. spanning the period 1916-2012. We employ both descriptive analysis and the ThresholdMinimum Dominating Set methodology from Graph Theory, to examine the evolution of inequality through time. In doing so, we use two alternative measures of inequality: the Top 1% share of income and the Gini coefficient. This...

As an indicator of social development and human capital, health has aroused ever-increasing concerns. Using CHNS2000 data, we attempt to address the following two issues: how could income inequality influence health; does the rising income inequality result in health inequality, especially will the health of the lower-income group get worse. We find that there is an “inverted-U” association bet...

in this paper, we extend some famous maximal inequalities and obtain strong laws of largenumbers for arbitrary random variables by use of these inequalities and martingale techniques.

In this note, we present an information diffusion inequality derived from an elementary argument, which gives rise to a very general Fano-type inequality. The latter unifies and generalizes the distance-based Fano inequality and the continuous Fano inequality established in [DW13, Corollary 1, Propositions 1 and 2], as well as the generalized Fano inequality in [HV94, Equation following (10)].

In this paper we recall with short proofs of some classical triangle inequalities, and prove corresponding non-Euclidean, i.e., spherical and hyperbolic versions of these inequalities. Among them are the well known Euler’s inequality, Rouché’s inequality (also called “the fundamental triangle inequality”), Finsler–Hadwiger’s inequality, isoperimetric inequality and others.