  This paper proposes a general framework for inference on three types of
almost dominances: Almost Lorenz dominance, almost inverse stochastic
dominance, and almost stochastic dominance. We first generalize almost Lorenz
dominance to almost upward and downward Lorenz dominances. We then provide a
bootstrap inference procedure for the Lorenz dominance coefficients, which
measure the degrees of almost Lorenz dominances. Furthermore, we propose almost
upward and downward inverse stochastic dominances and provide inference on the
inverse stochastic dominance coefficients. We also show that our results can
easily be extended to almost stochastic dominance. Simulation studies
demonstrate the finite sample properties of the proposed estimators and the
bootstrap confidence intervals. We apply our methods to the inequality growth
in the United Kingdom and find evidence for almost upward inverse stochastic
dominance.
