This paper proposes asymptotically distribution-free inference methods for comparing estimators which admit asymptotically linear Gaussian functional representations across dependent samples. The framework applies to a broad range of welfare indices used in inequality, poverty, and risk analysis. Two distinct situations are considered. First, we propose asymptotic and bootstrap in- tersection methods which are valid under arbitrary dependence between two samples. Second, we focus on the common case of overlapping samples—a special form of dependent samples where sample dependence arises solely from matched pairs—and provide asymptotic and bootstrap meth- ods for comparing indices. We derive consistent estimates for asymptotic variances using the influ- ence function approach. We study the finite-sample performance of the proposed methods through Monte Carlo simulations and find that confidence intervals based on overlapping samples exhibit satisfactory coverage rates and reasonable precision. In contrast, conventional methods based on the assumption of independent samples perform poorly in terms of coverage rates and interval widths. Asymptotic inference can be less reliable when dealing with heavy-tailed distributions, while the bootstrap method provides a viable remedy, unless the variance is substantial or fails to exist. The intersection method yields reliable results with arbitrary dependent samples, including settings in which the overlapping-sample assumptions do not hold. We demonstrate the practical applicability of our proposed methods in analyzing changes in household financial inequality in Italy over time.