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


Abstract in English

We present an elementary mathematical method to find the minimax estimator of the Bernoulli proportion $theta$ under the squared error loss when $theta$ belongs to the restricted parameter space of the form $Omega = [0, eta]$ for some pre-specified constant $0 leq eta leq 1$. 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.

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