  The allocation of limited resources to a large number of potential candidates
presents a pervasive challenge. In the context of ranking and selecting top
candidates from heteroscedastic units, conventional methods often result in
over-representations of subpopulations, and this issue is further exacerbated
in large-scale settings where thousands of candidates are considered
simultaneously. To address this challenge, we propose a new multiple comparison
framework that incorporates a modified power notion to prioritize the selection
of important effects and employs a novel ranking metric to assess the relative
importance of units. We develop both oracle and data-driven algorithms, and
demonstrate their effectiveness in controlling the error rates and achieving
optimality. We evaluate the numerical performance of our proposed method using
simulated and real data. The results show that our framework enables a more
balanced selection of effects that are both statistically significant and
practically important, and results in an objective and relevant ranking scheme
that is well-suited to practical scenarios.
