论文标题
无限方差下的Catoni风格的置信序列
Catoni-style Confidence Sequences under Infinite Variance
论文作者
论文摘要
在本文中，我们为不存在或无限的数据的方差提供了置信序列的扩展。置信序列提供的置信区间在任意数据依赖性停止时间时有效，自然具有广泛的应用。我们首先为有限方差案例的CATONI风格置信序列的宽度建立了一个下限，以突出现有结果的松动性。接下来，我们为具有放松界限的〜$ p^{th} - $时刻的数据分布而得出紧密的Catoni风格的置信序列，其中〜$ p \ in（1,2] $，并加强了〜$ p = 2 $的有限方差案例的结果。派生的结果比使用DubinS-Savavage Inquage Inquage Inquave offusitive caste the Pusitivest castections the the the bouts catoni stripers序列。
In this paper, we provide an extension of confidence sequences for settings where the variance of the data-generating distribution does not exist or is infinite. Confidence sequences furnish confidence intervals that are valid at arbitrary data-dependent stopping times, naturally having a wide range of applications. We first establish a lower bound for the width of the Catoni-style confidence sequences for the finite variance case to highlight the looseness of the existing results. Next, we derive tight Catoni-style confidence sequences for data distributions having a relaxed bounded~$p^{th}-$moment, where~$p \in (1,2]$, and strengthen the results for the finite variance case of~$p =2$. The derived results are shown to better than confidence sequences obtained using Dubins-Savage inequality.
