论文标题
$μ的有效置信区间，σ$只有一个观察结果
Valid confidence intervals for $μ, σ$ when there is only one observation available
论文作者
论文摘要
Portnoy（2019）考虑了基于单个观测值$ \，x \ sim {\ cal {n}}}（μ，\ \，σ^2）\，$，为平均值构建最佳置信区间的问题。在这里，我们将此结果扩展到获得$ \，σ\，$的1个样本置信区间，以及对称单形成分布的情况以及具有紧凑支持的分布。最后，我们扩展了Portnoy（2019）中的多元结果，以从$ \，m \，$的样本中，从$ m $ $ m $的多元正态分布中$ \，$，可能小于尺寸。
Portnoy (2019) considered the problem of constructing an optimal confidence interval for the mean based on a single observation $\, X \sim {\cal{N}}(μ, \, σ^2) \,$. Here we extend this result to obtaining 1-sample confidence intervals for $\, σ\,$ and to cases of symmetric unimodal distributions and of distributions with compact support. Finally, we extend the multivariate result in Portnoy (2019) to allow a sample of size $\, m \,$ from a multivariate normal distribution where $m$ may be less than the dimension.
