  This paper lays the groundwork for a unifying approach to stochastic
dominance testing under survey nonresponse that integrates the partial
identification approach to incomplete data and design-based inference for
complex survey data. We propose a novel inference procedure for restricted
$s$th-order stochastic dominance, tailored to accommodate a broad spectrum of
nonresponse assumptions. The method uses pseudo-empirical likelihood to
formulate the test statistic and compares it to a critical value from the
chi-squared distribution with one degree of freedom. We detail the procedure's
asymptotic properties under both null and alternative hypotheses, establishing
its uniform validity under the null and consistency against various
alternatives. Using the Household, Income and Labour Dynamics in Australia
survey, we demonstrate the procedure's utility in a sensitivity analysis of
temporal poverty comparisons among Australian households.
