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

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 Cramér 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 χ1 on the boundary of the null hypothesis. Finally, using the Cramér von Mises and likelihood ratio test statistics, preliminary simulations are conducted in which we compare our bootstrap method with the bootstrap empirical process procedure proposed in Linton, Song, and Whang (2010), in terms of size distortion and power. JEL Classification: C12; C13; C14;