顺序统计量的信息比较及其在拍卖和投票中的应用
Information Comparison of Order Statistics, with Applications to Auctions and Voting
AI总结：
研究从分布\(F(x\mid\theta)\)条件独立抽样样本中顺序统计量的信息含量，通过对数超模性判断准确性，扩展到多维比较，统一扩展拍卖信息聚合结果，为战略投票提供新方法。
AI中文摘要：
我们比较了在从分布\(F(x\mid\theta)\)进行条件独立抽样的样本中，随着样本量\(n\)增加时顺序统计量的信息含量。当且仅当累积反向风险\(-\log F(x\mid\theta)\)是对数超模时，\(n + 1\)次抽样中第\(k\)高的比\(n\)次抽样中第\(k\)高的更准确。对称地，当且仅当累积风险\(-\log(1 - F(x\mid\theta))\)是对数超模时，第\(k\)低的更准确。反转情况是例外，仅在经过递增变换后为指数位置实验的实验中出现。在大样本中，中间顺序统计量渐近完全信息，而有界的上下秩需要无界信息尾部条件。将分析从标量顺序统计量扩展到选定数据块，我们在风险率的对数超模性下获得多维比较。结果统一并扩展了拍卖中的信息聚合结果，并为战略投票提供了一种新的顺序统计方法。
英文摘要：
We compare the informativeness of order statistics in a sample of conditionally independent draws from a distribution \(F(x\midθ)\) as the sample size n increases. The k-th highest of n+1 draws is more accurate than the k-th highest of n if and only if the cumulative reverse hazard -\log F(x\midθ) is log-supermodular. Symmetrically, the k-th lowest is more accurate if and only if the cumulative hazard -\log(1-F(x\midθ)) is log-supermodular. Reversals are exceptional, occurring only for experiments that are, up to increasing transformations, exponential location experiments. In large samples, middle order statistics are asymptotically fully informative, while bounded lower and upper ranks require unbounded informativeness tail conditions. When full learning fails, bounded ranks converge to location experiments, and more central ranks are Blackwell more informative. Extending the analysis from scalar order statistics to blocks of selected data, we obtain multidimensional comparisons under log-supermodularity of hazard rates. The results unify and extend information-aggregation results in auctions and provide a new order-statistic approach to strategic voting.
