We propose a procedure for estimating the critical values of the extended Kolmogorov-Smirnov tests of Stochastic Dominance of arbitrary order in the general K-prospect case. We allow for the observations to be serially dependent and, for the first time, we can accommodate general dependence amongst the prospects which are to be ranked. Also, the prospects may be the residuals from certain conditional models, opening the way for conditional ranking. We also propose a test of Prospect Stochastic Dominance. Our method is based on subsampling and we show that the resulting tests are consistent and powerful against some N -½ local alternatives. We also propose some heuristic methods for selecting subsample size and demonstrate in simulations that they perform reasonably. We describe an alternative method for obtaining critical values based on recentring the test statistic and using full sample bootstrap methods. We compare the two methods in theory and in practice.

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A transformed metric entropy measure of dependence is studied which satisfies many desirable properties, including being a proper measure of distance. It is capable of good performance in identifying dependence even in possibly nonlinear time series, and is applicable for both continuous and discrete variables. A nonparametric kernel density implementation is considered here for many stylized models including linear and nonlinear MA, AR, GARCH, integrated series and chaotic dynamics. A related permutation test of independence is proposed and compared with several alternatives.

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In this paper we focus primarily on the dynamic evolution of the world distribution of growth rates in per capita GDP. We propose new concepts and measures of ''convergence,'' or ''divergence'' that are based on entropy distances and dominance relations between groups of countries over time.We update the sample period to include the most recent decade of data available, and we offer traditional parametric and new nonparametric estimates of the most widely used growth regressions for two important subgroups of countries, OECD and non-OECD. Traditional parametric models are rejected by the data, however, using robust nonparametric methods we find strong evidence in favor of ''polarization'' and ''within group'' mobility. r