Truthful Univariate Estimators
Truthful Univariate Estimators
复制标题
真实的单变量估计量
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Nisarg Shah
中科院分区：
文献类型：
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作者：
I. Caragiannis;Ariel D. Procaccia;Nisarg Shah
我们重温经典的问题，估计一个未知的单维分布的样本的人口平均值，采取博弈论的观点。在我们的环境中，样品由战略代理商提供，他们希望尽可能接近自己的价值。在这种情况下，样本均值会带来操纵机会，而样本中位数则不会。我们的关键问题是样本中位数是否是总体均值的最佳（就均方误差而言）真实估计。我们表明，当底层分布对称时，存在支配中位数的真实估计量。我们的主要结果是最坏情况下的最优真实估计，可证明优于中位数，可能是非对称分布的有界支持的表征。
We revisit the classic problem of estimating the population mean of an unknown single-dimensional distribution from samples, taking a game-theoretic viewpoint. In our setting, samples are supplied by strategic agents, who wish to pull the estimate as close as possible to their own value. In this setting, the sample mean gives rise to manipulation opportunities, whereas the sample median does not. Our key question is whether the sample median is the best (in terms of mean squared error) truthful estimator of the population mean. We show that when the underlying distribution is symmetric, there are truthful estimators that dominate the median. Our main result is a characterization of worst-case optimal truthful estimators, which provably outperform the median, for possibly asymmetric distributions with bounded support.