发表机构
Shanghai University of Finance and Economics; Syracuse University（上海财经大学; 雪城大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对二项Top-t选择问题，证明当k=2t时最不利位置最终中心化，否则其偏离对称中心的渐近表达式，通过容斥原理分析错误选择的二分图展开式。
AI 中文摘要
考虑k个独立的伯努利总体，每个总体被抽样n次，选择成功计数最大的t个总体，平局时采用均匀随机方式打破。经典单调性将分离度为δ的偏好区域的最坏情况简化为具有水平p和p+δ的滑移族，仅留下其绝对位置p∈[0,1−δ]未确定。高斯近似表明对称中心为p_c=(1−δ)/2，对于每个n≥2，精确的两总体问题唯一以该点为中心。对于固定的k、t和δ∈(0,1)，我们证明精确的最终中心化恰好当k=2t时成立。当k≠2t时，最不利位置p_{n,k,t}^*满足p_{n,k,t}^*−p_c=(k−2t)C_δ n^{-1/2}e^{-nΓ_δ}{1+o(1)}，其中C_δ和Γ_δ是显式正数。无论哪种情况，最不利位置最终都是唯一的。该证明将错误选择表示为两两误排序的并集，并应用容斥原理，得到二分图展开式。单次误排序的精确最大值在对称中心处，决定中心曲率；共享一个总体的两条边的交集通过其多重性不平衡决定中心斜率；其余所有图具有更高的大偏差率。
英文摘要
Consider $k$ independent Bernoulli populations, each sampled $n$ times, and select the $t$ populations with the largest success counts, breaking ties uniformly. Classical monotonicity reduces the worst case over the preference zone with separation $δ$ to the slippage family with levels $p$ and $p+δ$, leaving only its absolute location $p\in[0,1-δ]$ undetermined. A Gaussian approximation suggests the symmetric center $p_{\mathrm c}=(1-δ)/2$, and the exact two-population problem is uniquely centered there for every $n\ge2$. For fixed $k,t$ and $δ\in(0,1)$, we prove that exact eventual centering holds precisely when $k=2t$. When $k\ne2t$, the least-favorable location $p_{n,k,t}^*$ satisfies \[ p_{n,k,t}^*-p_{\mathrm c} =(k-2t)C_δn^{-1/2}e^{-nΓ_δ}\{1+o(1)\}, \] where $C_δ$ and $Γ_δ$ are explicit and positive. In either case, the least-favorable location is eventually unique. The proof writes incorrect selection as a union of pairwise misrankings and applies inclusion--exclusion, yielding a bipartite graph expansion. A single misranking has its exact maximum at the symmetric center and determines the central curvature; two-edge intersections sharing one population determine the central slope through their multiplicity imbalance; all remaining graphs have higher large-deviation rates.
