不确定数据下中位数分布的逼近及其它稳健估计
Approximating the Distribution of the Median and other Robust Estimators on Uncertain Data
摘要：
稳健估计，如点集的中位数，对于存在离群值的数据分析很重要。研究离散分布下位置不确定点的稳健估计。也就是说，数据集中的每个点都有一个描述其位置的离散概率分布。不确定数据的概率性质使得计算此类估计量具有挑战性，因为估计量的真实值现在由分布而不是单点描述。我们展示了如何构造和估计一个点集的中位数的分布。建立分布的近似支持需要近似线性的时间，而为该支持分配概率需要二次时间。我们还发展了一个一般的近似技术的分布的稳健估计的范围与有界VC维。这包括高维的几何中位数和线性回归的Siegel估计。
英文摘要：
Robust estimators, like the median of a point set, are important for data analysis in the presence of outliers. We study robust estimators for locationally uncertain points with discrete distributions. That is, each point in a data set has a discrete probability distribution describing its location. The probabilistic nature of uncertain data makes it challenging to compute such estimators, since the true value of the estimator is now described by a distribution rather than a single point. We show how to construct and estimate the distribution of the median of a point set. Building the approximate support of the distribution takes near-linear time, and assigning probability to that support takes quadratic time. We also develop a general approximation technique for distributions of robust estimators with respect to ranges with bounded VC dimension. This includes the geometric median for high dimensions and the Siegel estimator for linear regression.
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