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

This study proposes a distribution-free Bayesian procedure that detects infinite degrees of stochastic dominance (SD$\infty$) between two random outcomes and then seeks a finite degree $k\ge 1$ of stochastic dominance (SD$k$). 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$\infty$ and SD$k$ 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 SD$k$ and SD$\infty$ and compare them to the subsampling and bootstrap significance tests for SD$k$. Our simulation shows that the Bayesian tests for SD$k$ outperform the significance tests for small samples, especially for detecting non-stochastic dominance. This study shows that the test for SD$\infty$ is an accurate decision-making tool when using small samples.