论文标题
在限制参数空间中伯努利比例估算最小值的基本方法
An elementary approach for minimax estimation of Bernoulli proportion in the restricted parameter space
论文作者
论文摘要
我们提出了一种基本的数学方法，可以在平方误差下找到Bernoulli比例$θ$的最小值估计器，当$θ$属于表格$ω= [0，η] $的限制参数空间，用于某些预指定常数$ 0 \ leqη\ leq leq 1 $。从估计阳性COVID-19测试速率的问题启发了此问题。在统计或机器学习课程中教授点估算点时，提出的结果和应用将是教师和学生的有用材料。
We present an elementary mathematical method to find the minimax estimator of the Bernoulli proportion $θ$ under the squared error loss when $θ$ belongs to the restricted parameter space of the form $Ω= [0, η]$ for some pre-specified constant $0 \leq η\leq 1$. This problem is inspired from the problem of estimating the rate of positive COVID-19 tests. The presented results and applications would be useful materials for both instructors and students when teaching point estimation in statistical or machine learning courses.
