We consider a metric entropy capable of detecting deviations from symmetry that is suitable for both discrete and continuous processes. A test statistic is constructed from an integrated normed difference between nonparametric estimates of two density functions. The null distribution (symmetry)...

We examine the potential effect of naturalization on the U.S. immigrants's earnings. We find the earning gap between naturalized citizens and non-citizens is positive and a generally stable tent shape. We report a new entropy measure of the entire distribution gap, and conventional measures at...