纠缠单样本分布的均值估计

Ankit Pensia, Varun Jog, Po-Ling Loh
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引用次数: 2

摘要

当独立样本取自不相同的对称单峰分布时,我们考虑估计单变量数据的共同均值的问题。这捕获了所有样本都是高斯的设置,具有不同的未知方差。我们提出了一个适应数据异质性水平的估计器,在i.i.d.设置和一些异构设置中都实现了接近最优性,其中“低噪声”点的比例小到$\frac{{\log n}}{n}$。我们的估计量是经典统计中模态区间、短估计量和中值估计量的混合。速率取决于混合分布的百分位数,这使得我们的估计器即使对于方差无穷大的分布也是有用的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Mean estimation for entangled single-sample distributions
We consider the problem of estimating the common mean of univariate data, when independent samples are drawn from non-identical symmetric, unimodal distributions. This captures the setting where all samples are Gaussian with different unknown variances. We propose an estimator that adapts to the level of heterogeneity in the data, achieving near-optimality in both the i.i.d. setting and some heterogeneous settings, where the fraction of "low-noise" points is as small as$\frac{{\log n}}{n}$. Our estimator is a hybrid of the modal interval, shorth, and median estimators from classical statistics. The rates depend on the percentile of the mixture distribution, making our estimators useful even for distributions with infinite variance.
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