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We present an elementary mathematical method to find the minimax estimator ofthe Bernoulli proportion $\theta$ under the squared error loss when $\theta$belongs to the restricted parameter space of the form $\Omega = [0, \eta]$ forsome pre-specified constant $0 \leq \eta \leq 1$. This problem is inspired fromthe problem of estimating the rate of positive COVID-19 tests. The presentedresults and applications would be useful materials for both instructors andstudents when teaching point estimation in statistical or machine learningcourses.

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