An elementary approach for minimax estimation of Bernoulli proportion in the restricted parameter space

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.