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

Abstract

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 ≤ η ≤ 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.