This paper develops methodology for nonparametric estimation of a polarization measure due to Anderson (2004) and Anderson, Ge, and Leo (2006) based on kernel estimation techniques. We give the asymptotic distribution theory of our estimator, which in some cases is nonstandard due to a boundary...

The most popular general univariate polarization indices for discrete (Esteban and Ray 1994), and continuous (Duclos, Esteban and Ray 2004) variables are combined and extended to describe the extent of polarization between agents in a distribution defined over a collection of many discrete and...

The most popular general univariate polarization indexes for discrete and continuous variables are extended and combined to describe the extent of polarization between agents in a distribution defined over a collection of many discrete and continuous agent characteristics. A formula for the...

The cohesiveness of constituent nations in a confederation such as the Eurozone depends on their equally shared experiences. In terms of household incomes, commonality of distribution across those constituent nations with that of the Eurozone as an entity in itself is of the essence. Generally,...

Aphorisms that 'rising tides raise all boats' or that material advances of the rich eventually 'trickle down' to the poor are really maxims regarding the nature of stochastic processes that underlay the income/wellbeing paths of groups of individuals. This paper looks at the implications for the...

Aphorisms that "Rising tides raise all boats" or that material advances of the rich eventually "Trickle Down" to the poor are really maxims regarding the nature of stochastic processes that underlay the income/wellbeing paths of groups of individuals. This paper looks at the implications for the...

The burgeoning use of ordinal data throughout the Empirical Sciences calls for location and variation measurement instruments suitable for such data environments. Neither Pearson's Coefficient of Variation nor the Sharpe Ratio, relative variation comparison workhorses in cardinal worlds, are...

Measuring growth with ordered categorical variables is problematic due to their lack of cardinal measure and the equivocation and ambiguity inherent in the arbitrary attribution of cardinal scale to ordinal variates. Here, noting that the mean in a cardinal paradigm is the cumulation over its...

We propose several multivariate variance ratio statistics. We derive the asymptotic distribution of the statistics and scalar functions thereof under the null hypothesis that returns are unpredictable after a constant mean adjustment (i.e., under the Efficient Market Hypothesis). We do not...

In semiparametric models it is a common approach to under-smooth the nonparametric functions in order that estimators of the finite dimensional parameters can achieve root-n consistency. The requirement of under-smoothing may result as we show from inefficient estimation methods or technical...