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.

翻译：在大量潜在候选对象中分配有限资源是一个普遍存在的挑战。在从异方差单元中排序和选择最优候选对象时，传统方法往往导致子群体的过度代表，而当同时考虑数千个候选对象的大规模场景下，这一问题会进一步加剧。为应对这一挑战，我们提出了一种新的多重比较框架，该框架融入了一种改进的势(power)概念以优先选择重要效应，并采用一种新颖的排序度量来评估各单元的相对重要性。我们开发了基于理论最优( oracle )和基于数据的两种算法，并证明了它们在控制错误率和实现最优性方面的有效性。我们使用模拟数据和真实数据评估了所提方法的数值表现。结果表明，我们的框架能够更均衡地选择既具有统计显著性又具有实际重要性的效应，并产生一个客观且相关的排序方案，该方案非常适合实际应用场景。