Asymptotic and Bootstrap Tests for Infinite Order Stochastic Dominance Via the Method of Empirical Likelihood

Abstract

We develop asymptotic and bootstrap tests for stochastic dominance of the infinite order for distributions with known common support - the set of non-negative real numbers. These tests posit a null of dominance, which is characterized by an inequality in the corresponding Laplace transforms of the distribution functions. The bootstrap procedure uses a bootstrap data generating process that satisfies the two ”Golden Rules” of bootstrapping, and is obtained using constrained empirical likelihood estimation. To implement the constrained estimator, we develop a feasible-value-function approach as in Tabri and Davidson (2011). The proposed bootstrap tests are based on the weighted one-sided KolmogorovSmirnov and Cram´ er von Mises test statistics, which we show to be valid, and we also characterize the set of probabilities where the asymptotic size is exactly equal to the nominal level. Additionally, the asymptotic and bootstrap likelihood ratio tests are developed in which a Wilks phenomenon is unveiled. We prove that it is asymptotically distributed as 2 on the boundary of the null hypothesis. Finally, us