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

TL;DR

This paper introduces an elementary method for deriving the minimax estimator of a Bernoulli proportion within a restricted parameter space, with applications to COVID-19 test rate estimation.

Contribution

It provides a simple mathematical approach to find minimax estimators under parameter restrictions, enhancing teaching and understanding of point estimation in statistics.

Findings

Derives the minimax estimator for Bernoulli proportion in restricted space

Applicable to COVID-19 positive test rate estimation

Offers educational insights for teaching statistical estimation

Abstract

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.