Relative Distribution Methods

We present an outline of relative distribution methods, with an application to recent changes in the U.S. wage distribution. Relative distribution methods are a nonparametric statistical framework for analyzing data in a fully distributional context. The framework combines the graphical tools of exploratory data analysis with statistical summaries, decomposition, and inference. The relative distribution is similar to a density ratio. It is technically defined as the random variable obtained by transforming a variable from a comparison group by the cumulative distribution function (CDF) of that variable for a reference group. This transformation produces a set of observations, the relative data, that represent the rank of the original comparison value in terms of the reference group's CDF. The density and CDF of the relative data can therefore be used to fully represent and analyze distributional differences. Analysis can move beyond comparisons of means and variances to tap the detailed information inherent in distributions. The analytic framework is general and flexible, as the relative density is decomposable into the effect of location and shape differences, and into effects that represent both compositional changes in covariates, and changes in the covariate-outcome variable relationship.