Improved nonparametric bootstrap tests for weak joint stochastic dominance

The comparison of dependent random variables is pivotal across various domains, including poverty measurement and welfare evaluation. However, traditional stochastic dominance (SD) criteria neglect the dependency structure between variables, making them inadequate for comparing two dependent variables. To address this limitation, the concept of weak joint stochastic dominance (WJSD) has been introduced, offering deeper insights into the comparative magnitudes of dependent random variables. Nevertheless, previous studies have failed to established the accurate asymptotic properties of the statistics used for WJSD. Instead, these studies have relied on Monte Carlo method to estimate the upper boundaries of critical values, which may introduce potential inaccuracies. To mitigate these issues, this paper derives the asymptotic distribution of the WJSD statistic, verifies its consistency, and proposes an improved bootstrap methodology for precise p-value estimation. Our simulation studies reveal the enhanced performance of our method over traditional Monte Carlo methods, and its application to real data further highlights its practical applicability and relevance.