Testing higher and infinite degrees of stochastic dominance for small samples: A Bayesian approach

Abstract

This study proposes a distribution-free Bayesian procedure that detects infinite degrees of stochastic dominance (SD∞) between two random outcomes and then seeks a finite degree k≥1 of stochastic dominance (SDk). Based on small samples, we construct four-choice Bayesian tests by combining an encompassing prior Bayesian model with the Dirichlet process priors that discriminate between SD∞ and SDk of one random variable over the other with non-dominance or equality between them. We use Monte Carlo simulations to evaluate the novel Bayesian tests for SDk and SD∞ and compare them to the subsampling and bootstrap significance tests for SDk. Our simulation shows that the Bayesian tests for SDk outperform the significance tests for small samples, especially for detecting non-stochastic dominance. This study shows that the test for SD∞ is an accurate decision-making tool when using small samples.